Testing a new pain-reliever tablet. Refer to the Tropical

What are the treatments for a designed experiment that uses one qualitative factor with four levels—A, B, C, and D?

Problem 3E What is the difference between an observational experiment and a designed experiment?

Problem 4E What are the experimental units on which each of the following responses are observed? a. College GPA b. Household income c. Gasoline mileage rating for an automobile model d. Number of defective sectors on a computer disk e. December unemployment rate for a state

What are the treatments for a designed experiment with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?

Problem 5E Identifying the type of experiment. Brief descriptions of a number of experiments are given next. Determine whether each is observational or designed and explain your reasoning. a. An economist obtains the unemployment rate and gross state product for a sample of states over the past 10 years, with the objective of examining the relationship between the unemployment rate and the gross state product by census region. b. A manager in a paper production facility installs one of three incentive programs in each of nine plants to determine the effect of each program on productivity. c. A marketer of personal computers runs ads in each of four national publications for one quarter and keeps track of the number of sales that are attributable to each publication’s ad. d. An electric utility engages a consultant to monitor the discharge from its smokestack on a monthly basis over a 1-year period to relate the level of sulfur dioxide in the discharge to the load on the facility’s generators. e. Intrastate trucking rates are compared before and after governmental deregulation of prices changed, with the comparison also taking into account distance of haul, goods hauled, and the price of diesel fuel.

Exam performance study. Refer to the Teaching of Psychology (August 1998) study of whether a practice test helps students prepare for a final exam, Exercise 9.13 (p. 493). Recall that undergraduate students were grouped according to their class standing and whether they attended a review session or took a practice test prior to the final exam. The experimental design was a 3 X 2 factorial design, with Class Standing at three levels (low, medium, or high) and Exam Preparation at two levels (practice exam or review session). There were 22 students in each of the 3 X 2 = 6 treatment groups. After completing the final exam, each student rated his/ her exam preparation on an 11-point scale ranging from 0 (not helpful at all) to 10 (extremely helpful). The data for this experiment (simulated from summary statistics provided in the article) are saved in the accompanying file. The first 5 and last 5 observations in the data set are listed below. Conduct a complete analysis of the variance of the helpfulness rating data, including (if warranted) multiple comparisons of means. Do your findings support the research conclusion that “students at all levels of academic ability benefit from a…practice exam”?

Problem 6E Drafting NFL quarterbacks. Refer to the Journal of Productivity Analysis (Vol. 35, 2011) study of how successful NFL teams are in drafting productive quarterbacks, Exercise 1.16 (p. 25). Recall that the researchers measured two variables for each of the 331 quarterbacks drafted between 1970 and 2007: (1) Draft position (Top 10, between picks 11–50, or after pick 50) and (2) QB production score (where higher scores indicate more productive QBs). Suppose we want to compare the mean production score of quarterbacks in the three draft position groups. Identify each of the following elements for this study: a. Response variable b. Factor(s) c. Treatments d. Experimental units

Problem 7E Corporate sustainability and firm characteristics. Refer to the Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors, Exercise 1.26 (p. 27). Certified Public Accountants (CPAs) were surveyed on their firms’ likelihood of reporting sustainability policies (measured as a probability between 0 and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public or private): large/public, large/ private, small/public, and small/private. One goal of the analysis was to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type. Identify each of the following elements for this study: a. Experimental units b. Response variable c. Factor(s) d. Factor levels e. Treatments

Accounting and Machiavellianism. A study of Machiavellian traits in accountants was published in Behavioral Research in Accounting (January 2008). Recall (from Exercise 1.31, p. 27) that Machiavellian describes negative character traits such as manipulation, cunning, duplicity, deception, and bad faith. A Mach rating score was determined for each in a sample of accounting alumni of a large southwestern university. The accountants were then classified as having high, moderate, or low Mach rating scores. For one portion of the study, the researcher investigated the impact of both Mach score classification and gender on the average income of an accountant. For this experiment, identify each of the following: a. Experimental unit b. Response variable c. Factors d. Levels of each factor e. Treatments

Problem 9E Value perceptions of consumers. Refer to the Journal of Consumer Research study of whether between-store comparisons result in greater perceptions of value by consumers than within-store comparisons, Example 1.9 (p. 19). Recall that 50 consumers were randomly selected from all consumers in a designated market area to participate in the study. The researchers randomly assigned 25 consumers to read a within-store price promotion advertisement (“was $100, now $80”) and 25 consumers to read a between-store price promotion (“$100 there, $80 here”). The consumers then gave their opinion on the value of the discount offer on a 10-point scale (where 1 = lowest value and 10 = highest value). The goal was to compare the average discount values of the two groups of consumers. a. What is the response variable for this study? b. What are the treatments for this study? c. What is the experimental unit for this study?

Value perceptions of consumers. Refer to the Journal of Consumer Research study of whether between-store comparisons result in greater perceptions of value by consumers than within-store comparisons, Example 1.9 (p. 19). Recall that 50 consumers were randomly selected from all consumers in a designated market area to participate in the study. The researchers randomly assigned 25 consumers to read a within-store price promotion advertisement (“was $100, now $80”) and 25 consumers to read a between-store price promotion (“$100 there, $80 here”). The consumers then gave their opinion on the value of the discount offer on a 10-point scale (where 1 = lowest value and 10 = highest value). The goal was to compare the average discount values of the two groups of consumers. a. What is the response variable for this study? b. What are the treatments for this study? c. What is the experimental unit for this study?

Problem 12E Baker’s vs. brewer’s yeast. The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article on a comparison of two yeast extracts—baker’s yeast and brewer’s yeast. Brewer’s yeast is a surplus by-product obtained from a brewery; hence it is less expensive than primary-grown baker’s yeast. Samples of both yeast extracts were prepared at four different temperatures (45, 48, 51, and 54°C), and the autolysis yield (recorded as a percentage) was measured for each of the yeast-temperature combinations. The goal of the analysis was to investigate the impact of yeast extract and temperature on mean autolysis yield. a. Identify the factors (and factor levels) in the experiment. b. Identify the response variable. c. How many treatments are included in the experiment? d. What type of experimental design is employed?

Value perceptions of consumers (cont’d). Refer to Exercise 9.10. In addition to the factor, Type of advertisement (withinstore price promotion and between-store price promotion), the researchers also investigated the impact of a second factor— Location where ad is read (at home or in the store). About half of the consumers who were assigned to the within-store price promotion read the ad at home, and the other half read the ad in the store. Similarly, about half of the consumers who were assigned to the between-store price promotion read the ad at home, and the other half read the ad in the store. In this second experiment, the goal was to compare the average discount values of the groups of consumers created by combining Type of advertisement with Location. a. How many treatments are involved in this experiment? b. Identify the treatments.

Problem 13E Exam performance study. In Teaching of Psychology (August 1998), a study investigated whether final exam performance is affected by whether students take a practice test. Students in an introductory psychology class at Pennsylvania State University were initially divided into three groups based on their class standing: Low, Medium, or High. Within each group, students were randomly assigned to either attend a review session or take a practice test prior to the final exam. Thus, six groups were formed: (Low, Review), (Low, Practice exam), (Medium, Review), (Medium, Practice exam), (High, Review), and (High, Practice exam). One goal of the study was to compare the mean final exam scores of the six groups of students. a. What is the experimental unit for this study? b. Is the study a designed experiment? Why? c. What are the factors in the study? d. Give the levels of each factor. e. How many treatments are in the study? Identify them. f. What is the response variable?

Testing a new pain-reliever tablet. Paracetamol is the active ingredient in drugs designed to relieve mild to moderate pain and fever. To save costs, pharmaceutical companies are looking to produce paracetamol tablets from locally available materials. The properties of paracetamol tablets derived from khaya gum were studied in the Tropical Journal of Pharmaceutical Research (June 2003). Three factors believed to affect the properties of paracetamol tablets are (1) the nature of the binding agent, (2) the concentration of the binding agent, and (3) the relative density of the tablet. In the experiment, binding agent was set at two levels (khaya gum and PVP), binding concentration at two levels (.5% and 4.0%), and relative density at two levels (low and high). One of the dependent variables investigated in the study was tablet dissolution time (i.e., the amount of time [in minutes] for 50% of the tablet to dissolve). The goal of the study was to determine the effect of binding agent, binding concentration, and relative density on mean dissolution time. a. Identify the dependent (response) variable in the study. b. What are the factors investigated in the study? Give the levels of each. c. How many treatments are possible in the study? List them.

Problem 15E Use Tables V, VI, VII, and VIII in Appendix D to find each of the following F values: a. F .05, v1 = 4, v2 = 4 b. F .01, v1 = 4, v2 = 4 c. F .10, v1 = 30, v2 = 40 d. F .025, v1 = 15, v2 = 12

Find the following probabilities: a. \(P(F\ \leq\ 3.48) \text { for } v_{1}=5,\ v_{2}=9\) b. \(P(F\ >\ 3.09) \text { for } v_{1}=15,\ v_{2}=20\) c. \(P(F\ >\ 2.40) \text { for } v_{1}=15,\ v_{2}=15\) d. \(P(F\ \leq\ 1.83) \text { for } v_{1}=8,\ v_{2}=40\)

Problem 17E Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design. a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer. b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots. c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot. d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot. e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case? f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot. g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use ? = .05. h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?

Refer to Exercise 9.17. Conduct a two-sample t-test (Section 8.2) of the null hypothesis that the two treatment means are equal for each dot plot. Use \(\alpha\ =\ .05\) and two-tailed tests. In the course of the test, compare each of the following with the F-tests in Exercise 9.17: a. The pooled variances and the MSEs b. The t- and F-test statistics c. The tabled values of t and F that determine the rejection regions d. The conclusions of the t- and F-tests e. The assumptions that must be made to ensure the validity of the t- and F-tests

Refer to Exercises 9.17 and 9.18. Complete the following ANOVA table for each of the two dot plots:

A partially completed ANOVA table for a completely randomized design is shown here: a. Complete the ANOVA table. b. How many treatments are involved in the experiment? c. What is the total sample size, n, for the experiment? d. Use a random number generator to randomly assign each experimental unit to one of the treatments. Assume the sample size will be the same for each treatment. e. Do the data provide sufficient evidence to indicate a difference among the population means? Test using ? = .10. f. Find the approximate observed significance level for the test in part c and interpret it. g. Suppose that and . Do the data provide sufficient evidence to indicate a difference between and ? Assume that there are six observations for each treatment. Test using ? = .10. h. Refer to part g. Find a 90% confidence interval for . [Hint: Use as an estimate of both and ] i. Refer to part g. Find a 90% confidence interval for ?1. [Hint: Use as an estimate of .]

The data in the next table resulted from an experiment that used a completely randomized design. a. Use statistical software (or the appropriate calculation formulas in Appendix C) to complete the following ANOVA table: b. Test the null hypothesis that = = , where represents the true mean for treatment i, against the alternative that at least two of the means differ. Use ? = .01.

How workers respond to wage cuts. A randomized field experiment was carried out to determine how workers respond to wage cuts and the results published in Institute for the Study of Labor: Discussion Paper Series (March 2011). A company formed teams of two employees for a temporary promotion campaign. Both team members had identical individual tasks (sell promotional cards for entrance to a nightclub) and were initially paid the same hourly wage. After a short period of time on the job, teams were unknowingly randomly assigned to one of three treatments. In the “unilateral wage cut” treatment, one worker’s pay was cut by 25%; in the “general wage cut” treatment, both workers’ pay was cut by 25%; and in the “baseline” treatment, neither worker received a pay cut. The variable of interest was the decrease in the number of promotional cards sold after implementation of the pay cuts. The researchers wanted to know if the average decrease in cards sold differed depending on whether one or more of the workers received a pay cut. a. Identify the type of experimental design used in the study. b. Identify the dependent variable of interest. c. What is the factor in this experiment? The factor levels? d. Specify the null hypothesis of interest to the researchers. e. The ANOVA F-test was carried out and resulted in a p-value less than .001. Interpret these results using ? = .01.

Performance of a bus depot. The performances of public bus depots in India were evaluated and ranked in the International Journal of Engineering Science and Technology (February 2011). A survey was administered to 150 customers selected randomly and independently at each of three different bus depots (Depot 1, Depot 2, and Depot 3); thus, the total sample consisted of 450 bus customers. Based on responses to 16 different items (e.g., bus punctuality, seat comfort, luggage service, etc.), a performance score (out of 100 total points) was calculated for each customer. The average performance scores were compared across the three bus depots using an analysis of variance. The ANOVA F-test resulted in a p-value of .0001. a. Give details (experimental units, dependent variable, factor, treatments) on the experimental design utilized in this study. b. The researchers concluded that the “mean customer performance scores differed across the three bus depots at a 95% confidence level.” Do you agree?

Making high-stakes insurance decisions. The Journal of Economic Psychology (Sep. 2008) published the results of a high-stakes experiment where subjects (university students) were asked how much they would pay for insuring a valuable painting. The painting was threatened by both fire and theft, hence, the need for insurance. Of interest was the amount the subject was willing to pay (WTP) for insurance (thousands of dollars). For one part of the experiment, a total of 252 subjects were randomly assigned to one of three groups. Group 1 subjects () were informed of the hazards (both fire and theft) but were not told the exact probabilities of the hazards occurring. These subjects provided a separate WTP value for fire and theft. Group 2 subjects () were also informed of the hazards (fire/theft) and were not told the exact probabilities of the hazards occurring. However, these subjects provided a single WTP value covering both fire and theft. Group 3 subjects () were told of the hazards in sequential order (fire first, then theft). After being given the exact probability of fire occurring, the subjects provided a WTP value for fire. Then they were given the exact probability of theft occurring and were asked to provide a WTP value for theft. The researchers investigated whether the mean total WTP value differed for the three groups. a. Explain why the experimental design employed is a completely randomized design. b. Identify the dependent (response) variable and treatments for the design. c. Give the null and alternative hypotheses of interest to the researchers. d. Use a random number generator to randomly assign each of the 252 subjects to one of the three groups. Be sure to assign 84 subjects to each group.

Contingent valuation of homes in contaminated areas. Contingent valuation (CV) is a method of estimating property values that uses survey responses from potential homeowners. CV surveys were employed to determine the impact of contamination on property values in the Journal of Real Estate Research (Vol. 27, 2005). Homeowners were randomly selected from each of seven states—Kentucky, Pennsylvania, Ohio, Alabama, Illinois, South Carolina, and Texas. Each homeowner was asked to estimate the property value of a home located in an area contaminated by petroleum leaking from underground storage tanks (LUST). The dependent variable of interest was the LUST discount percentage (i.e., the difference between the current home value and estimated LUST value, as a percentage). The researchers were interested in comparing the mean LUST discount percentages across the seven states. a. Give the null and alternative hypotheses of interest to the researchers. b. An ANOVA summary table is shown below. Use the information provided to conduct the hypothesis test, part a. Use ?= .10.

Study of mutual fund performance. Mutual funds are classified as large-cap funds, medium-cap funds, or small-cap funds, depending on the capitalization of the companies in the fund. Hawaii Pacific University researchers S. Shi and M. Seiler investigated whether the average performance of a mutual fund is related to capitalization size (American Business Review, Jan. 2002). Independent random samples of 30 mutual funds were selected from each of the three fund groups, and the 90- day rate of return was determined for each fund. The data for the 90 funds were subjected to an analysis of variance, with the results shown in the ANOVA summary table below. a. State the null and alternative hypotheses for the ANOVA. b. Give the rejection region for the test using ? = .01. c. Make the appropriate conclusion using either the test statistic or the p-value.

Study of recall of TV commercials. Do TV shows with violence and sex impair memory for commercials? To answer this question, Iowa State researchers conducted a designed experiment in which 324 adults were randomly assigned to one of three viewer groups of 108 participants each (Journal of Applied Psychology, June 2002). One group watched a TV program with a violent content code (V) rating, the second group viewed a show with a sex content code (S) rating, and the last group watched a neutral TV program with neither a V nor an S rating. Nine commercials were embedded into each TV show. After viewing the program, each participant was scored on his or her recall of the brand names in the commercial messages, with scores ranging from 0 (no brands recalled) to 9 (all brands recalled). The data (simulated from information provided in the article) are saved in the accompanying file. The researchers compared the mean recall scores of the three viewing groups with an analysis of variance for a completely randomized design. a. Identify the experimental units in the study. b. Identify the dependent (response) variable in the study. c. Identify the factor and treatments in the study. d. The sample mean recall scores for the three groups were , , and . Explain why one should not draw an inference about differences in the population mean recall scores on the basis of only these summary statistics. e. An ANOVA on the data yielded the results shown in the Minitab printout on the next page. Locate the test statistic and p-value on the printout. f. Interpret the results from part e. using a = 0.01. What can the researchers conclude about the three groups of TV ad viewers? g. Check that the ANOVA assumptions are reasonably satisfied.

Does the media influence your attitude toward tanning? Dermatologists’ primary recommendation to prevent skin cancer is minimal exposure to the sun. Yet, models used in product advertisements are typically well tanned. Do such advertisements influence a consumer’s attitude toward tanning? University of California and California State University researchers designed an experiment to investigate this phenomenon and published their results in Basic and Applied Social Psychology (May 2010). College student participants were randomly assigned to one of three conditions: (1) view product advertisements featuring models with a tan, (2) view product advertisements featuring models without a tan, or (3) view products advertised with no models (control group). The objective was to determine whether the mean attitude toward tanning differs across the three conditions. A tanning attitude index (measured on a scale of 0 to 5 points) was recorded for each participant. The results are summarized in the accompanying table. a. Identify the type of experimental design utilized by the researchers. b. Identify the experimental units, dependent variable, and treatments for the design. c. Set up the null hypothesis for a test to compare the treatment means. d. The sample means shown in the table are obviously different. Explain why the researchers should not use these means alone to test the hypothesis, part c. e. The researchers conducted an ANOVA on the data and reported the following results: F = 3.60, p-value = .03. Carry out the test, part c. Use to draw your conclusion. f. What assumptions are required for the inferences derived from the test to be valid?

Income and road rage. Is a driver’s propensity to engage in road rage related to his or her income? Researchers at Mississippi State University attempted to answer this question by conducting a survey of a representative sample of over 1,000 U.S. adult drivers (Accident Analysis and Prevention, Vol. 34, 2002). Based on how often each driver engaged in certain road rage behaviors (e.g., making obscene gestures at, tailgating, and thinking about physically hurting another driver), a road rage score was assigned. (Higher scores indicate a greater pattern of road rage behavior.) The drivers were also grouped by annual income: under $30,000, between $30,000 and $60,000, and over $60,000. The data were subjected to an analysis of variance, with the results summarized in the table. Is there evidence to indicate that the mean road rage score differs for the three income groups? Test using ? = .05.

Effectiveness of sales closing techniques. Industrial sales professionals have long debated the effectiveness of various sales closing techniques. For example, a University of Akron study investigated the impact of five different closing techniques and a no-close condition on the level of a sales prospect’s trust in the salesperson (Industrial Marketing Management, Sept. 1996). More recently, a B2B Marketing Insider blog (Oct. 7, 2010) examined five currently- used sales closing techniques. Consider the following study. Sales scenarios are presented to a sample of 230 purchasing executives. Each subject received one of the five closing techniques or a scenario in which no close was achieved. After reading the sales scenario, each executive was asked to rate his/her level of trust in the salesperson on a 7-point scale. The table reports the six treatments employed in the study and the number of subjects receiving each treatment. a. Consider the following hypotheses: : The salesperson’s level of prospect trust is not influenced by the choice of closing method. : The salesperson’s level of prospect trust is influenced by the choice of closing method. Rewrite these hypotheses in the form required for an analysis of variance. b. Assume the ANOVA F-statistic is F = 2.21. Is there sufficient evidence to reject at ? = .05? c. What assumptions must be met for the test of part a to be valid? d. Would you classify this experiment as observational or designed? Explain.

Commercial eggs produced from different housing systems. In the production of commercial eggs in Europe, four different types of housing systems for the chickens are used: cage, barn, free range, and organic. The characteristics of eggs produced from the four housing systems were investigated in Food Chemistry (Vol. 106, 2008). Twenty-eight commercial grade A eggs were randomly selected from supermarkets—10 of which were produced in cages, 6 in barns, 6 with free range, and 6 organic. A number of quantitative characteristics were measured for each egg, including shell thickness (millimeters), whipping capacity (percent overrun), and penetration strength (newtons). The data (simulated from summary statistics provided in the journal article) are saved in the accompanying file. For each characteristic, the researchers compared the means of the four housing systems. Minitab descriptive statistics and ANOVA printouts for each characteristic are shown (next column). Fully interpret the results. Identify the characteristics for which the housing systems differ.

Animal-assisted therapy for heart patients. Chief executive officers of hospitals are adopting unconventional therapeutic methods to shorten the length of stay of patients. At an American Heart Association Conference (Nov. 2005), a study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients was presented. In the study, 76 heart patients were randomly assigned to one of three groups. Each patient in group T was visited by a human volunteer accompanied by a trained dog; each patient in group V was visited by a volunteer only; and the patients in group C were not visited at all. The anxiety level of each patient was measured (in points) both before and after the visits. The table below gives summary statistics for the drop in anxiety level for patients in the three groups. The mean drops in anxiety levels of the three groups of patients were compared using an analysis of variance. Although the ANOVA table was not provided in the article, sufficient information is provided to reconstruct it. a. Compute SST for the ANOVA, using the formula (see p. 496) where is the overall mean drop in anxiety level of all 76 subjects. b. Recall that SSE for the ANOVA can be written as where and are the sample variances associated with the three treatments. Compute SSE for the ANOVA. c. Use the results from parts a and b to construct the ANOVA table. d. Is there sufficient evidence (at ? = .01) of differences among the mean drops in anxiety levels by the patients in the three groups? e. Comment on the validity of the ANOVA assumptions. How might this affect the results of the study?

Is honey a cough remedy? Pediatric researchers at Pennsylvania State University carried out a designed study to test whether a teaspoon of honey before bed calms a child’s cough and published their results in Archives of Pediatrics and Adolescent Medicine (Dec. 2007). (This experiment was first described in Exercise 2.30, p. 61.) A sample of 105 children who were ill with an upper respiratory tract infection and their parents participated in the study. On the first night, the parents rated their children’s cough symptoms on a scale from 0 (no problems at all) to 6 (extremely severe) in five different areas. The total symptoms score (ranging from 0 to 30 points) was the variable of interest for the 105 patients. On the second night, the parents were instructed to give their sick children a dosage of liquid “medicine” prior to bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM)— an over-the-counter cough medicine—while others were given a similar dose of honey. Also, a third group of parents (the control group) gave their sick children no dosage at all. Again, the parents rated their children’s cough symptoms, and the improvement in total cough symptoms score was determined for each child. The data (improvement scores) for the study are shown in the accompanying table. The goal of the researchers was to compare the mean improvement scores for the three treatment groups. a. Identify the type of experimental design employed. What are the treatments? b. Conduct an analysis of variance on the data and interpret the results. c. Check the validity of the ANOVA assumptions.

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of assisting accounting students with their homework, Exercise 8.18 (p. 435). A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in the experiment. Recall that students took a pretest on a topic not covered in class and then each was given a homework problem to solve on the same topic. A completely randomized design was employed, with students randomly assigned to receive one of three different levels of assistance on the homework: (1) the completed solution, (2) check figures at various steps of the solution, and (3) no help at all. After finishing the homework, each student was given a posttest on the subject. The response variable of interest to the researchers was the knowledge gain (or, test score improvement), measured as the difference between the posttest and pretest scores. The data (simulated from descriptive statistics published in the article) are saved in the accompanying file. a. Give the null and alternative hypotheses tested in an analysis of variance of the data. b. Summarize the results of the analysis in an ANOVA table. c. Interpret the results, practically. Does your conclusion agree with the inferences drawn in Exercise 8.18?

Define an experimentwise error rate.

Define a comparisonwise error rate.

Consider a completely randomized design with k treatments. Assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. Determine the total number of pairwise comparisons for the following values of k. a. k = 3 b. k = 5 c. k = 4 d. k = 10

Problem 38E Consider a completely randomized design with five treatments, A, B, C, D, and E. The ANOVA F-test revealed significant differences among the means. A multiple comparisons procedure was used to compare all possible pairs of treatment means at ? = .05. The ranking of the five treatment means is summarized in each part below. Identify which pairs of means are significantly different.

A multiple comparison procedure for comparing four treatment means produced the confidence intervals shown here. Rank the means from smallest to largest. Which means are significantly different?

Performance of a bus depot. Refer to the International Journal of Engineering Science and Technology (February 2011) study of public bus depot performance, Exercise 9.23 (p. 508). Recall that 150 customers provided overall performance ratings at each of three different bus depots (Depot 1, Depot 2, and Depot 3). The average performance scores were determined to be significantly different at \(\alpha\) = .05 using an ANOVA F-test. The sample mean performance scores were reported as , \(\bar{x}_{1}=67.17, \bar{x}_{2}=58.95\), and \(\bar{x}_{3}=44.49\). The researchers employed the Bonferroni method to rank the three performance means using an experiment wise error rate of .05. Adjusted 95% confidence intervals for the differences between each pair of treatment means are shown in the table. Use this information to rank the mean performance scores at the three bus depots.

How workers respond to wage cuts. Refer to the Institute for the Study of Labor: Discussion Paper Series (March 2011) study of how workers respond to wage cuts, Exercise 9.22 (p. 508). Recall that teams of workers were divided into three wage cut groups: "unilateral wage cut," "general wage cut," and "baseline" (no wage cut). The researchers determined that the average decrease in promotional cards sold differed depending on the wage cut treatment group. Now the researchers want to rank the treatment means by making all possible pairwise comparisons. a. How many pairwise comparisons make up this phase of the study? List them. b. Why is a multiple comparisons procedure like Tukey's recommended for the analysis? c. The confidence interval for the difference between the means for "baseline" and "general wage cut," i.e., for \(\left(\mu_{\text {baseline }}-\mu_{\text {general }}\right)\),includes only positive values. Interpret this result.

Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on a problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making (see Exercise 3.44, p. 153). A sample of 77 volunteer students participated in one portion of the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, students were presented with a decision problem where the stated option had predominantly negative features (e.g., spending money on repairing a very old car). Prior to making the decision, the researchers asked each subject to list possible, more attractive alternatives. The researchers then compared the mean number of alternatives listed across the three emotional states with an analysis of variance for a completely randomized design. A partial ANOVA summary table is shown below. a. What conclusion can you draw from the ANOVA results? b. A multiple comparisons of means procedure was applied to the data using an experiment wise error rate of .05. Explain what the .05 represents. c. The multiple comparisons yielded the following results. What conclusion can you draw?

Does the media influence your attitude toward tanning? Refer to the Basic and Applied Social Psychology (May 2010) study of whether product advertisements influence consumers’ attitudes toward tanning, Exercise 9.29 (p. 510). Recall that college students were randomly assigned to one of three conditions—view product advertisements featuring models with a tan, view product advertisements featuring models without a tan, or view products advertised with no models. An ANOVA F-test revealed that the mean attitude toward tanning differed across the conditions. The researchers followed up this analysis with a multiple comparisons of means using an experiment wise error rate of .05. These results are summarized below. Fully interpret the results. Does it appear that the type of product advertisement can influence a consumer’s attitude toward tanning?

Study of recall of TV commercials. Refer to the Journal of Applied Psychology (June 2002) completely randomized design study to compare the mean commercial recall scores of viewers of three TV programs, presented in Exercise 9.28 (p. 509). Recall that one program had a violent content code (V) rating, one had a sex content code (S) rating, and one was a neutral TV program. Using Tukey’s method, the researchers conducted multiple comparisons of the three mean recall scores. a. How many pairwise comparisons were made in this study? b. The multiple comparison procedure was applied to the data and the results are shown in the Minitab printout at the bottom of the page. An experiment wise error rate of .05 was used. Locate the confidence interval for the comparison of the V and S groups. Interpret this result practically. c. Repeat part b for the remaining comparisons. Which of the groups has the largest mean recall score? d. In the journal article, the researchers concluded that “memory for [television] commercials is impaired after watching violent or sexual programming.” Do you agree?

A randomized block design yielded the following ANOVA table. a. How many blocks and treatments were used in the experiment? b. How many observations were collected in the experiment? c. Specify the null and alternative hypotheses you would use to compare the treatment means. d. What test statistic should be used to conduct the hypothesis test of part c? e. Specify the rejection region for the test of parts c and d. Use \(\alpha = .01\). f. Conduct the test of parts c–e and state the proper conclusion. g. What assumptions are necessary to ensure the validity of the test you conducted in part f? Text Transcription: alpha = .01

Study of mutual fund performance. Refer to the American Business Review (Jan. 2002) comparison of large-cap, medium-cap, and small-cap mutual funds, Exercise 9.26 (p. 509). Using an experimentwise error rate of .05, Tukey confidence intervals for the difference between mean rates of return for all possible pairs of fund types are given below. a. Why is the Tukey multiple comparisons method preferred over another method? b. Is there a significant difference between the treatment means for large-cap and medium-cap mutual funds? Explain. c. Is there a significant difference between the treatment means for large-cap and small-cap mutual funds? Explain. d. Is there a significant difference between the treatment means for medium-cap and small-cap mutual funds? Explain. e. Use your answers to parts b–d to rank the treatment means. f. Give a measure of reliability for the inference in part e.

An experiment was conducted using a randomized block design. The data from the experiment are displayed in the following table. a. Fill in the missing entries in the ANOVA table. b. Specify the null and alternative hypotheses you would use to investigate whether a difference exists among the treatment means. c. What test statistic should be used in conducting the test of part b? d. Describe the Type I and Type II errors associated with the hypothesis test of part b. e. Conduct the hypothesis test of part b using \(\alpha\ =\ .05\).

Effectiveness of sales closing techniques. Refer to the B2B Marketing Insider (Oct. 7, 2010) comparison of six sales closing techniques, Exercise 9.31 (p. 510). Assume the “level of trust” means for prospects of salespeople using each of the six closing techniques are listed in the table. A multiple comparisons of means analysis was conducted (at \(\alpha\) = .05), with the results shown in the third column of the table. Fully interpret the results.

A randomized block design was used to compare the mean responses for three treatments. Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to one experimental unit within each block. The data are shown in the next table, and the SPSS ANOVA printout for this experiment is shown below. a. Use the printout to fill in the entries in the following ANOVA table. b. Do the data provide sufficient evidence to indicate that the treatment means differ? Use \(\alpha\) = .05. c. Do the data provide sufficient evidence to indicate that blocking was effective in reducing the experimental error? Use \(\alpha\) = .05. d. Use the printout to rank the treatment means at \(\alpha\) = .05. e. What assumptions are necessary to ensure the validity of the inferences made in parts b, c, and d?

Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of treatments for children’s cough symptoms, Exercise 9.32 (p. 510). Do you agree with the statement (extracted from the article), “Honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection”? Perform multiple comparisons of means to answer the question.

Suppose an experiment employing a randomized block design has four treatments and nine blocks, for a total of \(4\ \times\ 9\ =\ 36\) observations. Assume that the Total Sum of Squares for the response is SS(Total) = 500. For each of the following partitions of SS(Total), test the null hypothesis that the treatment means are equal and test the null hypothesis that the block means are equal. Use \(\alpha\ =\ .05\) for each test. a. The Sum of Squares for Treatments (SST) is 20% of SS(Total), and the Sum of Squares for Blocks (SSB) is 30% of SS(Total). b. SST is 50% of SS(Total), and SSB is 20% of SS(Total). c. SST is 20% of SS(Total), and SSB is 50% of SS(Total). d. SST is 40% of SS(Total), and SSB is 40% of SS(Total). e. SST is 20% of SS(Total), and SSB is 20% of SS(Total).

Forecasting electrical consumption. Two different methods of forecasting monthly electrical consumption were compared and the results published in Applied Mathematics and Computation (Vol. 186, 2007). The two methods were Artificial Neural Networks (ANN) and Time Series Regression (TSR). Forecasts were made using each method for each of 4 months. These forecasts were also compared to the actual monthly consumption values. A layout of the design is shown in the accompanying table. The researchers want to compare the mean electrical consumption values of the ANN forecast, TSR forecast, and Actual consumption. a. Identify the experimental design employed in the study. b. A partial ANOVA table for the study is provided on the next page. Fill in the missing entries. c. Use the information in the table to conduct the appropriate ANOVA F-test using \(\alpha\ =\ .05\). State your conclusion in the words of the problem.

Peer mentor training at a firm. Peer mentoring occurs when a more experienced employee provides one-on-one support and knowledge sharing with a less experienced employee. The Journal of Managerial Issues (Spring 2008) published a study of the impact of peer mentor training at a large software company. Participants were 222 employees who volunteered to attend a 1-day peer mentor training session. One variable of interest was the employee’s level of competence in peer mentoring (measured on a 7-point scale). The competence level of each trainee was measured at three different times in the study: 1 week before training, 2 days after training, and 2 months after training. One goal of the experiment was to compare the mean competence levels of the three time periods. a. Explain why these data should be analyzed using a randomized block design. As part of your answer, identify the blocks and the treatments. b. A partial ANOVA table for the experiment is shown below. Explain why there is enough information in the table to make conclusions. c. State the null hypothesis of interest to the researcher. d. Make the appropriate conclusion. e. A multiple comparisons of means for the three time periods (using an experimentwise error rate of .10) is summarized below. Fully interpret the results.

Rotary oil rigs. An economist wants to compare the average monthly number of rotary oil rigs running in three states—California, Utah, and Alaska. In order to account for month-to-month variation, 3 months were randomly selected over a 2-year period, and the number of oil rigs running in each state in each month was obtained from data provided from World Oil (Jan. 2002) magazine. The data, reproduced in the accompanying table, were analyzed using a randomized block design. a. Why is a randomized block design preferred over a completely randomized design for comparing the mean number of oil rigs running monthly in California, Utah, and Alaska? b. Identify the treatments for the experiment. c. Identify the blocks for the experiment. d. State the null hypothesis for the ANOVA F-test. e. Locate the test statistic and p-value on the XLSTAT printout shown below. Interpret the results. f. A Tukey multiple comparisons of means (at ? = .05) is summarized in the XLSTAT printout below. Which state(s) have the significantly largest mean number of oil rigs running monthly?

Reducing on-the-job stress. Plant therapists believe that plants can reduce on-the-job stress. A Kansas State University study was conducted to investigate this phenomenon. Two weeks prior to final exams, 10 undergraduate students took part in an experiment to determine what effect the presence of a live plant, a photo of a plant, or absence of a plant has on a student’s ability to relax while isolated in a dimly lit room. Each student participated in three sessions—one with a live plant, one with a plant photo, and one with no plant (control). * During each session, finger temperature was measured at 1-minute intervals for 20 minutes. Because increasing finger temperature indicates an increased level of relaxation, the maximum temperature (in degrees) was used as the response variable. For example, one student’s finger measured 95.6° in the “Live Plant” condition, 92.6° in the “Plant Photo” condition, and 96.6° in the “No Plant” condition. The temperatures under the three conditions for the other nine students follow: Student 2 (95.6°, 94.8°, 96.0°), Student 3 (96.0°, 97.2°, 96.2°), Student 4 (95.2°, 94.6°, 95.7°), Student 5 (96.7°, 95.5°, 94.8°), Student 6 (96.0°, 96.6°, 93.5°), Student 7 (93.7°, 96.2°, 96.7°), Student 8 (97.0°, 95.8°, 95.4°), Student 9 (94.9°, 96.6°, 90.5°), Student 10 (91.4°, 93.5°, 96.6°). These data (based on data from Elizabeth Schreiber. Department of Statistics, Kansas State University, Manhattan, Kansas) are saved in the accompanying file. Conduct an ANOVA and make the proper inferences at ? = .10.

Absentee rates at a jeans plant. A plant that manufactures denim jeans in the United Kingdom introduced a computerized automated handling system. The new system delivers garments to the assembly line operators by means of an overhead conveyor. Although the automated system minimizes operator handling time, it inhibits operators from working ahead and taking breaks from their machine. A study in New Technology, Work, and Employment (July 2001) investigated the impact of the new handling system on worker absentee rates at the jeans plant. One theory is that the mean absentee rate will vary by day of the week, as operators decide to indulge in 1-day absences to relieve work pressure. Nine weeks were randomly selected, and the absentee rate (percentage of workers absent) determined for each day (Monday through Friday) of the workweek. The data are listed in the table on the next page. Conduct a complete analysis of the data to determine whether the mean absentee rate differs across the 5 days of the workweek.

Interactive video games and physical fitness. Wii Fit is an interactive video game marketed to consumers who want to increase their physical fitness level. The effectiveness of Wii Fit activities relative to other physical activities was investigated in the Journal of Physical Activity and Health (Vol. 7, 2010). A sample of 15 young adults (ages 21–38 years) participated in the study. Each adult completed a total of eight activities—rest, handheld gaming, Wii yoga, Wii muscle conditioning, Wii balance, Wii aerobics, brisk treadmill walking, and treadmill jogging. At the end of each session, the heart rate (beats per minute) of the participant was recorded. Since the goal was to compare mean heart rates across the eight activities, and since each adult completed all activities, a randomized block design ANOVA was conducted. a. Identify the treatments for this experiment. b. Identify the blocks for this experiment. c. The ANOVA F-test for treatments resulted in a p-value of .001. Interpret this result using ? = .01. d. Multiple comparisons (with an experiment wise error rate of .05) of the mean heart rates for the eight activities revealed the following. (Note: Means with the same letter are not significantly different.) Provide a ranking of the treatment means.

Suppose you conduct a \(4\ \times\ 3\) factorial experiment. a. How many factors are used in the experiment? b. Can you determine the factor type(s)—qualitative or quantitative—from the information given? Explain. c. Can you determine the number of levels used for each factor? Explain. d. Describe a treatment for this experiment and determine the number of treatments used. e. What problem is caused by using a single replicate of this experiment? How is the problem solved?

Stress in cows prior to slaughter. What is the level of stress (if any) that cows undergo prior to being slaughtered? To answer this question, researchers designed an experiment involving cows bred in Normandy, France (Applied Animal Behavior Science, June 2010). The heart rate (beats per minute) of a cow was measured at four different pre-slaughter phases—(1) first phase of visual contact with pen mates, (2) initial isolation from pen mates for prepping, (3) restoration of visual contact with pen mates, and (4) first contact with human prior to slaughter. Data for eight cows (simulated from information provided in the article) are shown in the accompanying table. The researchers analyzed the data using an analysis of variance for a randomized block design. Their objective was to determine whether the mean heart rate of cows differed in the four pre-slaughter phases. a. Identify the treatments and blocks for this experimental design. b. Conduct the appropriate analysis using a statistical software package. Summarize the results in an ANOVA table. c. Is there evidence of differences among the mean heart rates of cows in the four pre-slaughter phases? Test using \(\alpha\ =\ .05\). d. If warranted, conduct a multiple comparisons procedure to rank the four treatment means. Use an experiment wise error rate of \(\alpha\ =\ .05\).

The partially completed ANOVA for a factorial experiment with two replications is shown below. a. Complete the ANOVA table. b. Which sums of squares are combined to find the Sum of Squares for Treatments? Do the data provide sufficient evidence to indicate that the treatment means differ? Use ? = .05. c. Does the result of the test in part b warrant further testing? Explain. d. What is meant by factor interaction, and what is the practical implication if it exists? e. Test to determine whether these factors interact to affect the response mean. Use ? = .05 and interpret the result. f. Does the result of the interaction test warrant further testing? Explain.

A new method of evaluating health care research reports. When evaluating research reports in health care, a popular tool is the Assessment of Multiple Systematic Reviews (AMSTAR). AMSTAR, which incorporates 11 items (questions), has been widely accepted by professional health associations. A group of dental researchers has revised the assessment tool and named it R-AMSTAR (The Open Dentistry Journal, Vol. 4, 2010). The revised assessment tool was validated on five systematic reviews (named R1, R2, R3, R4, and R5) on rheumatoid arthritis. For each review, scores on the 11 R-AMSTAR items (all measured on a 4-point scale) were obtained. The data are shown in the table at the bottom of the page. a. One goal of the study was to compare the mean item scores of the five reviews. Set up the null and alternative hypotheses for this test. b. Examine the data in the table and explain why a randomized block ANOVA is appropriate to apply. c. The Minitab output for a randomized block ANOVA of the data (with Review as treatments and Item as blocks) appears below. Interpret the p-values of the tests shown. d. The Minitab printout also reports the results of a Tukey multiple comparison analysis of the five Review means. Which pairs of means are significantly different? Do these results agree with your conclusion in part c? e. The experimentwise error rate used in the analysis of part d is .05. Interpret this value.

Suppose a \(3\ \times\ 3\) factorial experiment is conducted with three replications. Assume that SS(Total) = 1,000. For each of the following scenarios, form an ANOVA table, conduct the appropriate tests, and interpret the results. a. The Sum of Squares of factor A main effect [SS(A)] is 20% of SS(Total), the Sum of Squares for factor B main effect [SS(B)] is 10% of SS(Total), and the Sum of Squares for interaction [SS(AB)] is 10% of SS(Total). b. SS(A) is 10%, SS(B) is 10%, and SS(AB) is 50% of SS(Total). c. SS(A) is 40%, SS(B) is 10%, and SS(AB) is 20% of SS(Total). d. SS(A) is 40%, SS(B) is 40%, and SS(AB) is 10% of SS(Total).

The following two-way table gives data for a factorial experiment with two observations for each factor-level combination. a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response variable as the y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors appear to interact? b. The Minitab ANOVA printout for this experiment is shown below. Sum the appropriate sums of squares and test to determine whether the treatment means differ at the ? = .05 level of significance. Does the test support your visual interpretation from part a? c. Does the result of the test in part b warrant a test for interaction between the two factors? If so, perform it using ? = .05. d. Do the results of the previous tests warrant tests of the two factor main effects? If so, perform them using ? = .05. e. Interpret the results of the tests. Do they support your visual interpretation from part a?

The next table gives data for a 2 X 2 factorial experiment with two observations per factor-level combination. a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response variable as the y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors appear to interact? b. Use the computational formulas in Appendix C to create an ANOVA table for this experiment. c. Test to determine whether the treatment means differ at the \(\alpha = .05\) level of significance. Does the test support your visual interpretation from part a? d. Does the result of the test in part b warrant a test for interaction between the two factors? If so, perform it using \(\alpha = .05\). e. Do the results of the previous tests warrant tests of the two factor main effects? If so, perform them using \(\alpha = .05\). Yes. f. Interpret the results of the tests. Do they support your visual interpretation from part a? g. Given the results of your tests, which pairs of means, if any, should be compared? Text Transcription: alpha = .05

The partially complete ANOVA table given here is for a two-factor factorial experiment. a. Give the number of levels for each factor. b. How many observations were collected for each factor level combination? c. Complete the ANOVA table. d. Test to determine whether the treatment means differ. Use \(\alpha\ =\ .10\). e. Conduct the tests of factor interaction and main effects, each at the \(\alpha\ =\ .10\) level of significance. Which of the tests are warranted as part of the factorial analysis? Explain.

Eggshell quality in laying hens. Introducing calcium into a hen’s diet can improve the shell quality of the eggs laid. One way to do this is with a limestone diet. In Animal Feed Science and Technology (June 2010), researchers investigated the effect of hen’s age and limestone diet on eggshell quality. Two different diets were studied—fine limestone (FL) and coarse limestone (CL). Hens were classified as either younger hens (24–36 weeks old) or older hens (56–68 weeks old). The study used 120 younger hens and 120 older hens. Within each age group, half the hens were fed a fine limestone diet and the other half a coarse limestone diet. Thus, there were 60 hens in each of the four combinations of age and diet. The characteristics of the eggs produced from the laying hens were recorded, including shell thickness. a. Identify the type of experimental design employed by the researchers. b. Identify the factors and the factor levels (treatments) for this design. c. Identify the experimental unit. d. Identify the dependent variable. e. The researchers found no evidence of factor interaction. Interpret this result, practically. f. The researchers found no evidence of a main effect for hen’s age. Interpret this result, practically. g. The researchers found statistical evidence of a main effect for limestone diet. Interpret this result, practically. (Note: The mean shell thickness for eggs produced by hens on a CL diet was larger than the corresponding mean for hens on an FL diet.)

Baker’s vs. brewer’s yeast. The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article on a comparison of two yeast extracts, baker’s yeast and brewer’s yeast. Brewer’s yeast is a surplus by-product obtained from a brewery, hence it is less expensive than primary-grown baker’s yeast. Samples of both yeast extracts were prepared at four different temperatures (45, 48, 51, and 54°C); thus, a 2 X 4 factorial design with yeast extract at two levels and temperature at four levels was employed. The response variable was the autolysis yield (recorded as a percentage). NW a. How many treatments are included in the experiment? b. An ANOVA found sufficient evidence of factor interaction at \(\alpha = .05\). Interpret this result practically. c. Give the null and alternative hypotheses for testing the main effects of yeast extract and temperature. d. Explain why the tests, part c, should not be conducted. e. Multiple comparisons of the four temperature means were conducted for each of the two yeast extracts. Interpret the results shown below. Text Transcription: alpha = .05

Insomnia and education. Many workers suffer from stress and chronic insomnia. Is insomnia related to education status? Researchers at the Universities of Memphis, Alabama at Birmingham, and Tennessee investigated this question in the Journal of Abnormal Psychology (Feb. 2005). Adults living in Tennessee were selected to participate in the study using a random-digit telephone dialing procedure. In addition to insomnia status (normal sleeper or chronic insomnia), the researchers classified each participant into one of four education categories (college graduate, some college, high school graduate, and high school dropout). One dependent variable of interest to the researchers was a quantitative measure of daytime functioning called the Fatigue Severity Scale (FSS). The data were analyzed as a \(2\ \times\ 4\) factorial experiment, with Insomnia status and Education level as the two factors. a. Determine the number of treatments for this study. List them. b. The researchers reported that “the Insomnia \(\times\) Education interaction was not statistically significant.” Practically interpret this result. (Illustrate with a graph.) c. The researchers discovered that the sample mean FSS for people with insomnia was greater than the sample mean FSS for normal sleepers, and this difference was statistically significant. Practically interpret this result. d. The researchers reported that the main effect of Education was statistically significant. Practically interpret this result. e. Refer to part d. In a follow-up analysis, the sample mean FSS values for the four Education levels were compared using Tukey’s method (\(\alpha\ =\ .05\)), with the results shown below. What do you conclude?

Purchase of fair-trade products. “Just-world” theory proposes that people receive the rewards and/or punishments that they deserve. Marketing researchers examined just-world theory in the context of fair trade (Journal of Marketing, January 2012). In particular, the researchers wanted to know if manipulating market conditions has an impact on whether consumers purchase fair-trade products. A designed experiment with two manipulated market factors was employed. One factor was justice reparation potential (low or high); a second factor was producer need (moderate or high). A sample of business students was divided into four groups—34 students were randomly assigned to each of the \(2\ \times\ 2\) market condition treatments. After reading a news article and press release that manipulated their condition, each student reported on their intention to purchase a fair-trade product. Intention was measured on a scale ranging from 0 to 6 points. The data for all 136 students (simulated based on information provided in the journal article) are saved in the accompanying file. An ANOVA for the data is shown in the accompanying Minitab printout. a. For this designed experiment, explain (practically) what it means to have factor interaction. b. Conduct the F-test for factor interaction using \(\alpha\ =\ .01\). What do you conclude? c. In the journal article, the researchers reported on the ANOVA F-tests for main effects. Is this necessary? Explain. d. A plot of the sample means for the four treatments is shown below in the Minitab graph. Explain why this graph supports your answer to part b. e. The researchers hypothesized that when justice restoration potential is low, fair-trade purchase intentions will be lower when Need is high rather than moderate. Conversely, when justice restoration potential is high, purchase intentions will be greater when Need is high rather than moderate. Is there evidence to support this theory?

Corporate social responsibility study. The importance that consumers place on the social responsibility of firms has grown over the past decade. As a consequence, corporations are developing more socially responsible strategies and procedures (e.g., corporate sustainability, fair-trade policies). The perceptions consumers have of these strategies were investigated in the Journal of Marketing (November 2009). Undergraduate marketing students were provided information on a firm’s irresponsible behaviors as well as public statements made by the firm to promote its corporate social responsibility policy. Each student then rated the level of hypocrisy in the statements on a 7-point scale. Students were divided into groups depending on the type of statement they were given (concrete or abstract) and on the order of information provided (statement first or corporate behavior first). The researchers analyzed the data using a \(2\ \times\ 2\) factorial design. a. Identify the factors and treatments in this experiment. b. An ANOVA F-test for the interaction between statement type and order of information was found to be significant (p-value < .01). Practically interpret this result. c. The means for the four treatments are shown in the table. Graph these means to demonstrate the nature of the interaction. d. Based on the result, part b, advise the researchers on whether or not they should perform main effect tests.

Problem 77E Testing a new pain-reliever tablet. Refer to the Tropical Journal of Pharmaceutical Research (June 2003) study of the impact of binding agent, binding concentration, and relative density on the mean dissolution time of pain-relief tablets, Exercise 9.14 (p. 493). Recall that the binding agent was set at two levels (khaya gum and PVP), binding concentration at two levels (.5% and 4.0%), and relative density at two levels (low and high); thus, a 2 * 2 * 2 factorial design was employed. The sample mean dissolution times for the treatments associated with the factors binding agent and relative density when the other factor (binding concentration) is held fixed at .5% are , and Do the results suggest there is an interaction between binding agent and relative density? Explain.

Insomnia and education. Many workers suffer from stress and chronic insomnia. Is insomnia related to education status? Researchers at the Universities of Memphis, Alabama at Birmingham, and Tennessee investigated this question in the Journal of Abnormal Psychology (Feb. 2005). Adults living in Tennessee were selected to participate in the b. Give a practical interpretation of the test for interaction using ? = .05. c. The F-values (and corresponding p-values) missing in the table were not provided in the journal article. Are these results required to complete the analysis of the data? Explain. d. In a follow-up to the ANOVA, the researchers compared the mean willing to pay values for the homogeneous and mixed-menu conditions at each level of the order condition. In the virtue condition, the mean for the homogeneous menu ($11.08) was significantly lower than the mean for the mixed menu ($13.26). In the vice condition, the mean for the homogeneous menu ($17.11) was significantly higher than the mean for the mixed menu ($15.00). Demonstrate why these results support your answer to part b. Illustrate with a graph.

Eyewitnesses and mugshots. When an eyewitness to a crime examines a set of mugshots at a police station, the photos are usually presented in groups (e.g., six mugshots at a time). Criminologists at Niagara University investigated whether mugshot group size has an effect on the selections made by eyewitnesses (Applied Psychology in Criminal Justice, April 2010). A sample of 90 college students was shown a video of a simulated theft. Shortly thereafter, each student was shown 180 mugshots and asked to select a photo that most closely resembled the thief. (Multiple photos could be selected.) The students were randomly assigned to view either 3, 6, or 12 mugshots at a time. Within each mugshot group size, the students were further randomly divided into three sets. In the first set, the researchers focused on the selections made in the first 60 photos shown; in the second set, the focus was on selections made in the middle 60 photos shown; and in the third set, selections made in the last 60 photos were recorded. The dependent variable of interest was the number of mugshot selections. Simulated data for this 3 X 3 factorial ANOVA, with mugshot group size at three levels (3, 6, or 12 photos) and photo set at three levels (first 60, middle 60, and last 60) are saved in the accompanying file. Fully analyze the data for the researchers. In particular, the researchers want to know if mugshot group size has an effect on the mean number of selections, and, if so, which group size leads to the most selections. Also, are there a higher number of selections made in the first 60, middle 60, or last 60 photos viewed?

Commercial eggs produced from different housing systems. Refer to the Food Chemistry (Vol. 106, 2008) study of four different types of egg housing systems, Exercise 9.33 (p. 511). Recall that the four housing systems were cage, barn, free range, and organic. In addition to housing system, the researchers also determined the weight class (medium or large) for each sampled egg. The data on whipping capacity (percent overrun) for the 28 sampled eggs are shown in the accompanying table. The researchers want to investigate the effect of both housing system and weight class on the mean whipping capacity of the eggs. In particular, they want to know whether the difference between the mean whipping capacity of medium and large eggs depends on the housing system. a. Identify the factors and treatments for this experiment. b. Use statistical software to conduct an ANOVA on the data. Report the results in an ANOVA table. c. Is there evidence of interaction between housing system and weight class? Test using ? = .05. [Hint: Due to an unbalanced design, you will need to analyze the data using the general linear model procedure of your statistical software.] What does this imply, practically? d. Interpret the main effect test for housing system (using ? = .05). What does this imply, practically? e. Interpret the main effect test for weight class (using ? = .05). What does this imply, practically?

Impact of flavor name on consumer choice. Do consumers react favorably to products with ambiguous colors or names? Marketing Professors E. G. Miller and B. E. Kahn investigated this phenomenon in the Journal of Consumer Research (June 2005). As a “reward” for participating in an unrelated experiment, 100 consumers were told they could have some jelly beans available in several cups on a table. Half the consumers were assigned to take jelly beans with common descriptive flavor names (e.g., watermelon green), while the other half were assigned to take jelly beans with ambiguous flavor names (e.g., monster green). Within each group, half of the consumers took the jelly beans and left (low cognitive load condition), while the other half were distracted with additional questions designed to distract them while they were taking their jelly beans (high cognitive load condition). Consequently, a 2 X 2 factorial experiment was employed— with Flavor Name (common or ambiguous) and Cognitive Load (low or high) as the two factors—with 25 consumers assigned to each of four treatments. The dependent variable of interest was the number of jelly beans taken by each consumer. The means and standard deviations of the four treatments are shown in the accompanying table. a. Calculate the total of the n = 25 measurements for each of the four categories in the 2 X 2 factorial experiment. b. Calculate the correction for mean, CM. (See Appendix C for computational formulas.) c. Use the results of parts a and b to calculate the sums of squares for Load, Name, and Load X Name interaction. d. Calculate the sample variance for each treatment. Then calculate the sum of squares of deviations within each sample for the four treatments. e. Calculate SSE. (Hint: SSE is the pooled sum of squares for the deviations calculated in part d.) f. Now that you know SS(Load), SS(Name), SS(Load X Name), and SSE, find SS(Total). g. Summarize the calculations in an ANOVA table. h. The researchers reported the F-value for Load X Name interaction as F = 5.34. Do you agree? i. Conduct a complete analysis of these data. Use \(\alpha = .05\) for any inferential techniques you employ. Illustrate your conclusions graphically. j. What assumptions are necessary to ensure the validity of the inferential techniques you used? State them in terms of this experiment. Text Transcription: alpha = .05

TV ad recall study. Refer to the Journal of Applied Psychology (June 2002) study of the effect of violence and sex on a television viewer’s ability to recall a TV commercial, Exercise 9.28 (p. 509). Recall that 324 adults were randomly assigned to one of three TV content groups, with 108 subjects in each group. One group watched a TV program with a violent content code (V) rating; the second group viewed a show with a sex content code (S) rating, and the last group watched a neutral TV program. Commercials were embedded into each TV show, and after the participants viewed the show, the advertisement recall score was measured for each participant. In addition, the researchers recorded whether or not the subject had previously seen the commercial. The layout for the full experimental design is shown in the accompanying schematic. Note that there are two factors in this experiment—TV content group at three levels and watched commercial before status at two levels—and the design is a 3 X 2 factorial. The researchers want to know whether the two factors, TV content group and watched commercial before status, impact the mean recall score. Conduct a two-way factorial analysis of variance on the data saved in the accompanying file. The researchers concluded that (1) the Neutral TV content group has the highest mean recall score, but that there is no significant difference between the mean recall scores of the Violent and Sex content groups, and (2) there is no significant difference between the mean recall scores of those who had previously watched the commercial and those who had not. Do you agree?

On the trail of the cockroach. Knowledge of how cockroaches forage for food is valuable for companies that develop and manufacture roach bait and traps. Many entomologists believe, however, that the navigational behavior of cockroaches scavenging for food is random. D. Miller of Virginia Tech University challenged the “random-walk” theory by designing an experiment to test a cockroach’s ability to follow a trail of their fecal material (Explore, Research at the University of Florida, Fall 1998). A methanol extract from roach feces—called a pheromone— was used to create a chemical trail. German cockroaches were released at the beginning of the trail, one at a time, and a video surveillance camera was used to monitor the roach’s movements. In addition to the trail containing the fecal extract (the treatment), a trail using methanol only (the control) was created. To determine if trail-following ability differed among cockroaches of different age, sex, and reproductive status, four roach groups were used in the experiment: adult males, adult females, gravid (pregnant) females, and nymphs (immatures). Twenty roaches of each type were randomly assigned to the treatment trail, and 10 of each type were randomly assigned to the control trail. Thus, a total of 120 roaches were used in the experiment. The movement pattern of each cockroach was measured (in “pixels”) as the average trail deviation. The data for the 120 cockroaches in the study are stored in the accompanying file. (The first 5 and last 5 observations in the data set are listed here.) Conduct a complete analysis of the data. Determine whether roaches can distinguish between the fecal extract and control trail and whether trail-following ability differs according to age,

What is the difference between a one-way ANOVA and a two-way ANOVA?

Explain the difference between an experiment that employs a completely randomized design and one that employs a randomized block design.

Why does the experimentwise error rate of a multiple comparisons procedure differ from the significance level for each comparison (assuming the experiment has more than two treatments)?

A completely randomized design is used to compare four treatment means. The data are shown in the table. Given that SST = 36.95 and SS(Total) = 62.55, complete an ANOVA table for this experiment. b. Is there evidence that the treatment means differ? Use ? = .10. c. Place a 90% confidence interval on the mean response for treatment 4.

What are the treatments in a two-factor experiment, with factor A at three levels and factor B at two levels?

An experiment employing a randomized block design was conducted to compare the mean responses for four treatments—A, B, C, and D. The treatments were randomly assigned to the four experimental units in each of five blocks. The data are shown in the following table. a. Given that SS(Total) = 22.31 and SS(Block) = 10.688 and SSE = .288, complete an ANOVA table for the experiment. b. Do the data provide sufficient evidence to indicate a difference among treatment means? Test using \(\alpha\) = .05 c. Does the result of the test in part b warrant further comparison of the treatment means? If so, how many pairwise comparisons need to be made? d. Is there evidence that the block means differ? Use \(\alpha\) = .05.

Ethics of salespeople. Within marketing, the area of personal sales has long suffered from a poor ethical image, particularly in the eyes of college students. An article in Journal of Business Ethics (Vol. 15, 1996) investigated whether such opinions by college students are a function of the type of sales job (high tech vs. low tech) and/or the sales task (new account development vs. account maintenance). Four different samples of college students were confronted with the four different situations (new account development in a high-tech sales task, new account development in a low-tech sales task, account maintenance in a high-tech sales task, and account maintenance in a low-tech sales task) and were asked to evaluate the ethical behavior of the salesperson on a 7-point scale ranging from 1 (not a serious ethical violation) to 7 (a very serious ethical violation). Identify each of the following elements of the experiment: a. Response b. Factor(s) and factor level(s) c. Treatments d. Experimental units

The following table shows a partially completed ANOVA table for a two-factor factorial experiment. a. Complete the ANOVA table. b. How many levels were used for each factor? How many treatments were used? How many replications were performed? c. Find the value of the Sum of Squares for Treatments. Test to determine whether the data provide evidence that the treatment means differ. Use . d. Is further testing of the nature of factor effects warranted? If so, test to determine whether the factors interact. Use Interpret the result.

Problem 91SE Impact of paper color on exam scores. A study published in Teaching Psychology (May 1998) examined how external clues influence student performance. Undergraduate students were randomly assigned to one of four different midterm examinations. Form 1 was printed on blue paper and contained difficult questions, while form 2 was also printed on blue paper but contained simple questions. Form 3 was printed on red paper, with difficult questions; form 4 was printed on red paper with simple questions. The researchers were interested in the impact that Color (red or blue) and Question (simple or difficult) had on mean exam score. a. What experimental design was employed in this study? Identify the factors and treatments. b. The researchers conducted an ANOVA and found a significant interaction between Color and Question (p-value <.03). Interpret this result. c. The sample mean scores (percentage correct) for the four exam forms are listed in the table above. Plot the four means on a graph to illustrate the Color * Question interaction.

Robots trained to behave like ants. Robotic researchers investigated whether robots could be trained to behave like ants in an ant colony (Nature, Aug. 2000). Robots were trained and randomly assigned to “colonies” (i.e., groups) consisting of 3, 6, 9, or 12 robots. The robots were assigned the task of foraging for “food” and to recruit another robot when they identified a resource-rich area. One goal of the experiment was to compare the mean energy expended (per robot) of the four different colony sizes. a. What type of experimental design was employed? b. Identify the treatments and the dependent variable. c. Set up the null and alternative hypotheses of the test. d. The following ANOVA results were reported: F = 7.70, numerator df = 3, denominator df = 56, p-value < .001. Conduct the test at a significance level of \(\alpha\ =\ .05\) and interpret the result. e. Multiple comparisons of mean energy expended for the four colony sizes were conducted using an experiment-wise error rate of .05. The results are summarized below. How many pairwise comparisons are conducted in this analysis? f. Refer to part e. Interpret the results shown in the table.

Flower production of dwarf shrubs. Dwarf shrubs are popular with model home landscapers. Stetson University researchers conducted an experiment to determine the effects of fire on the shrub’s growth (Florida Scientist, Spring 1997). Twelve experimental plots of land were selected in a pasture where the shrub is abundant. Within each plot, three dwarf shrubs were randomly selected and treated as follows: one shrub was subjected to fire, another to clipping, and the third was left unmanipulated (a control). After 5 months, the number of flowers produced by each of the 36 shrubs was determined. The objective of the study was to compare the mean number of flowers produced by dwarf shrubs for the three treatments (fire, clipping, and control). a. Identify the type of experimental design employed, including the treatments, response variable, and experimental units. b. Illustrate the layout of the design using a graphic similar to Figure 9.20. c. The ANOVA of the data resulted in a test statistic of F = 5.42 for treatments, with an associated p-value of p = .009. Interpret this result. d. The three treatment means were compared using Tukey’s method at \(\alpha\ =\ .05\). Interpret the results shown below.

Fortune’s E-50 list. The Fortune E-50 is a listing of the top 50 electronic commerce and Internet-based companies, as determined by Fortune magazine each year. Fortune groups the companies into four categories: (1) e-companies, (2) Internet software and service, (3) Internet hardware, and (4) Internet communication. Consider a study to compare the mean rates of return for the stock of companies in the four Fortune categories. Because the age of an electronic commerce or Internet-based company may have an impact on rate of return, the study is designed to remove any age variation. Four 1-year-old companies, four 3-year-old companies, and four 5-year-old companies were selected; within each age group, one company was randomly selected from category 1, one from category 2, one from category 3, and one from category 4. a. What type of experimental design is employed? b. Identify the key elements of the experiment (i.e., treatments, blocks, response variable, and experimental unit).

College tennis recruiting with a team Website. Most university athletic programs now have a Website with information on individual sports and a Prospective Student Athlete Form that allows high school athletes to submit their academic and sports achievements directly to the college coach. The Sport Journal (Winter 2004) published a study of how important team Web sites are to the recruitment of college tennis players. A survey was conducted of NCAA tennis coaches, of which 53 were from Division I schools, 20 were from Division II schools, and 53 were from Division III schools. Coaches were asked to respond to a series of statements, including “The Prospective Student Athlete Form on the Web site contributes very little to the recruiting process.” Responses were measured on a 7-point scale (where 1 = strongly disagree and 7 = strongly agree). In order to compare the mean responses of tennis coaches from the three NCAA divisions, the data were analyzed with a completely randomized design ANOVA. a. Identify the experimental unit, dependent (response) variable, factor, and treatments for this study. b. Give the null and alternative hypotheses for the ANOVA F-test. c. The observed significance level of the test was found to be p-value < .003. What conclusion can you draw if you want to test at \(\alpha\) = .05? d. The mean responses are listed and ranked in the next table. The results were obtained using a multiple comparisons procedure with an experimentwise error rate of .05. Interpret the results practically.

Effectiveness of geese decoys. What type of decoy should you purchase for hunting waterfowl? A study in the Journal of Wildlife Management (July 1995) compared the effectiveness of three different decoy types—taxidermy mounted decoys, plastic shell decoys, and full-bodied plastic decoys—in attracting Canada geese to sunken pit blinds. In order to account for an extraneous source of variation, three pit blinds were used as blocks in the experiment. Thus, a randomized block design with three treatments (decoy types) and three blocks (pit blinds) was employed. The response variable was the percentage of a goose flock to approach within 46 meters of the pit blind on a given day. The data are given in the table.* A Minitab printout of the analysis follows. Locate the p-value for treatments on the printout and interpret the result.

Removing bacteria from water. A coagulation-microfiltration process for removing bacteria from water was investigated in Environmental Science & Engineering (Sept. 1, 2000). Chemical engineers at Seoul National University performed a designed experiment to estimate the effect of both the level of the coagulant and acidity (pH) level on the coagulation efficiency of the process. Six levels of coagulant (5, 10, 20, 50, 100, and 200 milligrams per liter) and six pH levels (4.0, 5.0, 6.0, 7.0, 8.0, and 9.0) were employed. Water specimens collected from the Han River in Seoul, Korea, were placed in jars, and each jar was randomly assigned to receive one of the \(6\ \times\ 6 = 36\) combinations of coagulant level and pH level. a. What type of experimental design was applied in this study? b. Give the factors, factor levels, and treatments for the study.

Leadership style and subordinate behavior. Leadership acts occur when one person tries to influence the behavior of others toward the attainment of some goal. The effects of leadership style on the behavior of subordinates were investigated in Accounting, Organizations and Society (Vol. 20, 1995). Four types of leadership style were defined based on two variables: the degree of control applied (high or low) and the level of consideration shown for subordinates (high or low). A sample of 257 senior auditors in Big-Six accounting firms yielded the following distribution of leadership styles for the auditors’ leaders: All subjects were asked to indicate (confidentially) how frequently their auditing fieldwork had been intentionally substandard in a particular way. They were asked to respond using a scale that ranged from 1 (never) to 5 (always). These data are summarized in the following table. An ANOVA conducted to test for differences in the four treatment means yielded F = 30.4. a. Do the data indicate that leadership style affects the behavior of subordinates? Test using \(\alpha\ =\ .05\). b. The Bonferroni multiple comparisons procedure was used to rank the four treatment means at an experimentwise error rate of \(\alpha\ =\ .05\). Carefully interpret the results shown in the table. c. What assumptions must hold to ensure the validity of the Bonferroni procedure?

Study of anticoagulant drugs. Three anticoagulant drugs are studied to compare their effectiveness in dissolving blood clots. Each of five subjects receives the drugs at equally spaced time intervals and in random order. Time periods between drug applications permit a drug to be passed out of a subject’s body before the subject receives the next drug. After each drug is in the bloodstream, the length of time (in seconds) required for a cut of specified size to stop bleeding is recorded. The results are shown in the following table. a. What type of experimental design was used in this study? Identify the response, factor(s), factor type(s), treatments, and experimental units. b. Is there evidence of a difference in mean clotting time among the three drugs? Test using ? = .10. c. What is the observed significance level of the test you conducted in part a? Interpret it. d. Was blocking effective in reducing the variation among the data? That is, do the data support the contention that the mean clotting time varies from person to person? e. If warranted, use a multiple comparisons technique to determine whether one of the drugs is most effective. Use an overall significance level of ? = .10.

A managerial decision problem. A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by estimating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton, or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were pulled from each of five cartons of a typical shipment and weighed. The weights (in pounds) are shown in the table. a. Identify the response, factor(s), treatments, and experimental units. b. Do these data provide sufficient evidence to indicate differences in the mean weight per brochure among the five cartons? c. What assumptions must be satisfied in order for the test of part b to be valid? d. Use Tukey’s method to compare all pairs of means, with a = .05 as the overall level of significance. e. Given the results, make a recommendation to management about whether to sample from one carton or from many cartons.

Steel ingot quality study. A quality-control supervisor measures the quality of a steel ingot on a scale of 0 to 10. He designs an experiment in which three different temperatures (ranging from 1,100 to 1,200 \(^\circ F\)) and five different pressures (ranging from 500 to 600 psi) are used, with 20 ingots produced at each Temperature-Pressure combination. Identify the following elements of the experiment: a. Response b. Factor(s) and factor type(s) c. Treatments d. Experimental units

Factors that impact a customer’s willingness to buy. Advancements in information technology have yielded services that compete against products, with each providing roughly the same benefits to the consumer (e.g., home answering machines and voice-mail services). With the advent of such services, consumers also face different types of pricing schemes. Using a \(2\ \times\ 2\) factorial design, D. Fortin and T. Greenlee of the University of Rhode Island investigated the effects of the type of message retrieval system (answering machine vs. voice-mail service) and the type of pricing (lump sum amount for 5 years of use vs. monthly cost for 5 years of use) on consumers’ willingness to buy (Journal of Business Research, Vol. 41, 1998). The first pricing option requires the consumer to do mental arithmetic to determine the total cost of the system; the second provides the true full cost. Thirty subjects were randomly assigned to each of the four treatments. Each was exposed to a purchase situation involving the relevant product or service and payment description and was asked to indicate his or her willingness to buy the item on a 5-point scale (1 = definitely would not buy; 5 = definitely would buy). The results are presented in the incomplete ANOVA table below. a. Fill in the degrees of freedom (df) column in the ANOVA table. b. Specify the null and alternative hypotheses that should be used in testing for interaction effects between type of message retrieval system and pricing option. c. Conduct the test of part b using \(\alpha\ =\ .05\). Interpret the results in the context of the problem. d. Given the results of part c, is it advisable to conduct main effects tests? Why or why not? If so, perform the appropriate main effects tests using \(\alpha\ =\ .05\).

Ethics of downsizing. A major strategic alternative for many U.S. firms is to reduce the size of their workforce, i.e., to “downsize.” The ethics of downsizing decisions from the employees’ perspective was investigated in the Journal of Business Ethics (Vol. 18,1999). The researchers surveyed a sample of 209 employees who were enrolled in an Executive MBA Program or weekend program at one of three Colorado universities. These individuals were divided into five distinct groups, depending on their job situation at a previous or current firm. The groups were named (1) Casualties, (2) Survivors, (3) Implementors/casualties, (4) Implementors/survivors, and (5) Formulators. The sampled employees completed a questionnaire on their ethical perceptions of downsizing. One item asked employees to respond to the statement: “It is unethical for a downsizing decision to be announced or implemented on or prior to a major holiday.” Responses were measured using a 5-point Likert scale, where 1 = strongly agree, 2 = agree, 3 = neutral, 4 = disagree, and 5 = strongly disagree. Data on both the qualitative variable “Group” and the quantitative variable “Ethics response” are saved in the accompanying file. The researchers’ goal was to determine if any differences exist among the mean ethics scores for the five groups. a. The data were analyzed using an ANOVA for a completely randomized design. Identify the factor, treatments, response variable, and experimental units for this design. b. Specify the null and alternative hypotheses tested. c. A Minitab printout of the ANOVA is displayed on the next page. Can you conclude that the mean ethics scores of the five groups of employees are significantly different? Explain. d. Access the data and check that the assumptions required for the ANOVA F-test are reasonably satisfied. e. Multiple comparisons of the treatment (group) means were conducted using the Bonferroni method with an experimentwise error rate of .05. Explain why the Bonferroni method is preferred over another multiple comparisons method (e.g., Tukey or Scheffé). f. Refer to part e. Determine the number of pairwise comparisons for this analysis. g. The sample mean ethics scores for the five groups and Bonferroni rankings are summarized below. Identify the groups with the significantly largest mean ethics scores.

Diamonds sold at retail. Refer to the Journal of Statistics Education study of 308 diamonds for sale on the open market, Exercise 2.157 (p. 117). Recall that the file contains information on the quantitative variables, size (number of carats) and price (in dollars), and on the qualitative variables, color (D, E, F, G, H, and I), clarity (IF, VS1, VS2, VVS1, and VVS2), and independent certification group (GIA, HRD, or IGI). Select one of the quantitative variables and one of the qualitative variables. a. Set up the null and alternative hypotheses for determining whether the means of the quantitative variable differ for the levels of the qualitative variable. b. Use the data to conduct the test, part a, at ? = 10. State the conclusion in the words of the problem. c. Check any assumptions required for the methodology used in part b to be valid. d. Follow up the analysis with multiple comparisons of the treatment means. Use an experimentwise error rate of .05. Interpret the results practically.

Participation in a company’s walking program. A study was conducted to investigate the effect of prompting in a walking program instituted at a large corporation (Health Psychology, Mar. 1995). Five groups of walkers—27 in each group— agreed to participate by walking for 20 minutes at least one day per week over a 24-week period. The participants were prompted to walk each week via telephone calls, but different prompting schemes were used for each group. Walkers in the control group received no prompting phone calls; walkers in the “frequent/low” group received a call once a week with low structure (i.e., “just touching base”); walkers in the “frequent/high” group received a call once a week with high structure (i.e., goals are set); walkers in the “infrequent/low” group received a call once every 3 weeks with low structure; and walkers in the “infrequent/high” group received a call once every 3 weeks with high structure. The table at the bottom of the page lists the number of participants in each group who actually walked the minimum requirement each week for weeks 1, 4, 8, 12, 16, and 24. The data were subjected to an analysis of variance for a randomized block design, with the five walker groups representing the treatments and the six time periods (weeks) representing the blocks. a. What is the purpose of blocking on weeks in this study? b. Fill in the missing entries on the ANOVA summary table shown above. c. Is there sufficient evidence of a difference in the mean number of walkers per week among the five walker groups? Use \(\alpha\ =\ .05\). d. Tukey’s technique was used to compare all pairs of treatment means with an experimentwise error rate of \(\alpha\ =\ .05\). The rankings are shown at the bottom of the page. Interpret these results. e. What assumptions must hold to ensure the validity of the inferences in parts c and d?

Testing the effectiveness of supermarket sales strategies. Factorial designs are commonly employed in marketing research to evaluate the effectiveness of sales strategies. At one supermarket, two of the factors were price level (regular, reduced price, cost to supermarket) and Display level (normal display space, normal display space plus end-of-aisle display, twice the normal display space). A 3 × 3 complete factorial design was employed, where each treatment was applied three times to a particular product at a particular supermarket. The dependent variable of interest was unit sales for the week. (To minimize treatment carryover effects, each treatment was preceded and followed by a week in which the product was priced at its regular price and was displayed in its normal manner.) The next table reports the data collected. a. How many treatments are considered in this study? b. Do the data indicate that the mean sales differ among the treatments? Test using ? = .10. c. Is the test of interaction between the factors price and Display warranted as a result of the test in part b? If so, conduct the test using ? = .10. d. Are the tests of the main effects for Price and Display warranted as a result of the previous tests? If so, conduct them using ? = .10. e. Which pairs of treatment means should be compared as a result of the tests in parts b–d?

Problem 105SE Manager’s trust and job-related tension. Research published in Accounting, Organizations and Society (Vol. 19, 1994) investigated whether the effects of different performance evaluation styles (PES) on the level of job-related tension is affected by trust. Three performance evaluation styles were considered. Each is related to the way in which accounting information is used for the purpose of evaluation. The three styles are budget-constrained (BC), profit-conscious (PC), and the non accounting style (NA), which focuses on factors such as quality of output and attitude toward the job. Consider a questionnaire (similar to the one used in the study) administered to 200 managers. It measures the performance evaluation style of each manager’s superior (on a 10-point scale), the manager’s job-related tension, and the manager’s level of trust (low, medium, and high) in his or her superior. These data were used to produce the partial ANOVA table and table of treatment means shown next. a. Describe the treatments of this study. b. Complete the ANOVA table. c. Investigate the presence of an interaction effect by conducting the appropriate hypothesis test using ? = .05. d. Use a plot of treatment means to investigate the interaction effect. Interpret your results. Are your results of parts c and d consistent? e. Given your answers to parts c and d, should the F-tests for the two main effects be conducted?

Improving the output of an industrial lathe. Quality Engineering (Vol. 6, 1994) reported the results of an experiment that was designed to find ways to improve the output of an industrial lathe. The lathe is controlled by a computer that automatically feeds bar stock, cuts the stock, machines the surface finish, and releases the part. As it is machined, the bar stock spins and is held in place by a collet. The lathe operator sets the feed (the rate at which bars are machined) and the speed (spin rate). The product characteristic of interest is surface finish. It is measured on a gauge that records the vertical distance a probe travels as it moves along a given horizontal distance on the bar. The rougher the surface, the higher the gauge measurement. The factors that were manipulated in the experiment were speed, feed, collet tightness, and tool wear. The table below reports the factor-level settings and the resulting surface finish measurements (H = High; L = Low). a. What type of experimental design was used? b. How many different treatments were applied? c. Perform an ANOVA for these data. d. Do significant interaction effects exist? Test using \(\alpha\) = .05. Interpret your results. e. Is it necessary to perform main effect tests? Why or why not? If so, perform the tests using \(\alpha\) = .05. f. What assumptions must hold to ensure the validity of your results in parts c, d, and e?

Testing a new insect repellent. Traditionally, people protect themselves from mosquito bites by applying insect repellent to their skin and clothing. Research suggests that permethrin, an insecticide with low toxicity to humans, can provide protection from mosquitoes. A study in the Journal of the American Mosquito Control Association (Mar. 1995) investigated whether a tent sprayed with a commercially available 1% permethrin formulation would protect people, both inside and outside the tent, against biting mosquitoes. Two canvas tents—one treated with permethrin, the other untreated—were positioned 25 meters apart on flat, dry ground in an area infested with mosquitoes. Eight people participated in the experiment, with four randomly assigned to each tent. Of the four stationed at each tent, two were randomly assigned to stay inside the tent (at opposite corners) and two to stay outside the tent (at opposite corners). During a specified 20-minute period during the night, each person kept count of the number of mosquito bites received. The goal of the study was to determine the effect of both Tent type (treated or untreated) and Location (inside or outside the tent) on the mean mosquito bite count. a. What type of design was employed in the study? b. Identify the factors and treatments. c. Identify the response variable. d. The study found statistical evidence of interaction between Tent type and Location. Give a practical interpretation of this result.

Suppose you conduct a 4 X 3 factorial experiment. a. How many factors are used in the experiment? b. Can you determine the factor type(s)—qualitative or quantitative—from the information given? Explain. c. Can you determine the number of levels used for each factor? Explain. d. Describe a treatment for this experiment and determine the number of treatments used. e. What problem is caused by using a single replicate of this experiment? How is the problem solved?