?Lighting Effect on Plant Growth Which type of light results in the tallest rosemary plants after 38 days of growth? To answer this question, Joliet Ju

Find the critical value from the Studentized range distribution for: (a) a = 0.05, n = 16, k = 7 (b) a = 0.05, n = 30, k = 6 (c) a = 0.01, n = 42, k = 4 Note: Use q0.01,40,4 since q0.01,42,4 is not in the table. (d) Find the critical value from the Studentized range distribution for H0: m1 = m2 = m3 = m4 = m5 = m6, with n = 46, a = 0.05

Suppose that there is sufficient evidence to reject H0: m1 = m2 = m3 = m4 using a one-way ANOVA. The mean square error from ANOVA is determined to be 373. The sample means are x1 = 78, x2 = 64, x3 = 70, x4 = 47, with n1 = n2 = n3 = n4 = 31. Use Tukey’s test to determine which pairwise means are significantly different using a familywise error rate of a = 0.05.

Soil Testing A researcher took water samples from a stream running through a forest and groundwater in the forest. The samples were collected over the course of a year. Each sample was analyzed for the concentration of dissolved organic carbon (mg/L) in it and categorized according to the type of water collected. Water was collected from streams (surface water), groundwater was collected from organic soil, and groundwater was collected from mineral soil. The researcher wanted to determine if the mean concentration of dissolved organic carbon was the same for each collection area. The results are presented in the following table. (a) What is the response variable in this study? (b) What is the factor? How many levels of treatment does the factor have? (c) State the null and alternative hypotheses. (d) A normal probability plot of each sample (organic, mineral, and surface) indicates the data come from a normally distributed population. Use the following summary statistics from StatCrunch to verify the equal population standard deviation requirement. (e) Use the following StatCrunch output to test if the means are the same at the a = 0.01 level of significance. (f) Interpret the P-value. (g) Shown are side-by-side boxplots of each type of collection area drawn in StatCrunch. Do the boxplots support the analytic results? Which collection area type appears to differ from the rest? (h) The following display represents the results of Tukey’s test obtained from StatCrunch. Which pairwise means differ?

Grading Timber Desiring to grade timber mechanically, engineers studied the modulus of rupture in \(\mathrm{lb} / \text {in.}^{2}\), for a sample of untreated green, 7 inch by 9 inch, mixed oak timbers, sorted by grade: select structural, No. 1, No. 2, and below grade. A one-way ANOVA was performed to test \(H_{0:}: \mu_{\text {select }}=\mu_{\mathrm{No} .1}=\mu_{\mathrm{No} .2}=\mu_{\text {below grade }}\). The null hypothesis was rejected with a P-value of 0.018. The engineers proceeded to conduct Tukey’s test to determine which pairwise means differed using Minitab. The results are presented next. Which pairwise means differ? What do you conclude from the test? Note: 1 = select structural, 2 = No. 1, 3 = No. 2, and 4 = below grade. Text Transcription: ln/in^2 H_0 : mu_select = mu_No.1 = mu_No.2 = mu_below grade

Seating Choice versus GPA In a study of students at Lewis & Clark Community College, a professor compared the chosen seat location of students in mathematics courses to their overall grade point average (GPA). He randomly selected 10 students from each of three seat locations: (1) front, (2) middle, and (3) back. The GPAs follow: (a) Explain why this data may be analyzed using a one-way ANOVA. (b) Test the null hypothesis that the mean score for each location is the same at the a = 0.05 level of significance. (c) If the null hypothesis is rejected in part (a), use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05. (d) Draw boxplots of the three treatment levels to support the analytic results obtained in parts (b) and (c).

Catapults Four different catapult designs are being tested for their ability to launch water balloons. The experimenter decides to block by person firing. The distances (in feet) achieved for each catapult are given. (a) What is the response variable in this study? (b) Explain why it makes sense to block by person firing the catapult. (c) Test H0: m1 = m2 = m3 = m4 against H1: at least one of the means is different, where m1 is the mean for the Mark IV V2, m2 is the mean for the Balloon Ballista, and so on, at the a = 0.05 level of significance. (d) If the null hypothesis from part (c) was rejected, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05. (e) Draw boxplots of the data for each catapult design using the same scale to support the analytical results obtained in parts (c) and (d).

Defensive Driving An investigator for the state police wants to determine the effectiveness of three different defensive driving training programs to see if there are gender differences. Five subjects of each gender who recently received speeding tickets are assigned to each program. At the end of the program, each is given a written test on his or her knowledge of defensive driving. The scores (out of 100) are given next. (a) The scores are approximately normally distributed. Verify the requirement of equal population variances. (b) Determine whether there is significant interaction between program and gender. (c) If there is no significant interaction, determine whether there is significant difference in the means for the three programs. (d) Draw an interaction plot of the data to support the results of parts (b) and (c). (e) If there is significant difference in the means for the three programs, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05.

Many fast-food restaurants use automatic soft-drink dispensing machines that fill cups once an order is placed at a drive-through window. A regional manager for a fast-food chain wants to determine if the machines in his region are dispensing the same amount of product. He samples four different machines and measures a random sample of 16-ounce drinks from each machine. (a) Do the data indicate that the mean amount dispensed from the machines is not the same? Use an a = 0.05 level of significance. (b) Use Tukey’s test, if necessary, to determine which pairwise means differ using a familywise error rate of a = 0.05. (c) Draw boxplots of the four treatment levels to support your conclusions in parts (a) and (b).

Lighting Effect on Plant Growth Which type of light results in the tallest rosemary plants after 38 days of growth? To answer this question, Joliet Junior College student Michael Bueno planted 90 rosemary seeds in plant pods. He randomly assigned each seed to a green, blue, or red light bulb. All the seeds were planted in the same type of soil, received the same amount of water and same amount of light each day, and were all located in a room maintained at 70 degrees Fahrenheit. The following data represent the heights (in inches) of the plants after 38 days. (a) What type of experimental design did Michael perform? (b) What is the response variable in his experiment? Is it quantitative or qualitative? (c) What is the explanatory variable in his experiment? Is it quantitative or qualitative? (d) What other factors did Michael identify that may affect plant growth? How did he handle these factors? (e) What technique was used to address the fact that some seeds may grow at different rates? In other words, just as not all humans grow to the same height, all rosemary seeds will not grow to the same height (due to genetics). What did Michael do to address this concern? (f) Michael wanted to know whether the color of the light played a role in determining plant height after 38 days. State the null and alternative hypotheses. (g) Following are the descriptive statistics for each treatment group. Is the requirement of equal population variances satisfied? Why? (h) Use the results of a one-way ANOVA from Minitab given next to test the hypotheses stated in part (f). (i) In the next column are side-by-side boxplots of each plant’s growth for each light color. Based on the boxplots and the results of part (h), do you believe a certain light color promotes plant growth more than the others? (j) Following are the results of Tukey’s test. Determine which pairwise means may differ using a familywise error rate of a = 0.05.

A rock climber wants to test the tensile strength of three different types of braided ropes. She knows that the rope thickness can make a difference, so she decides to block by thickness. The tensile strengths for each rope type are given next (a) Test H0: m1 = m2 = m3 against H1: at least one of the means is different, where m1 is the mean for the nylon braided rope, m2 is the mean for the polyester braided rope, and m3 is the mean for the polypropylene braided rope, at the a = 0.05 level of significance. (b) If the null hypothesis from part (a) was rejected, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05. (c) Draw boxplots of the data for each treatment using the same scale to support the analytical results obtained in parts (a) and (b).

A manufacturing researcher wants to determine if age or gender significantly affects the time required to learn an assembly line task. He randomly selected 24 adults aged 20 to 64 years old, of whom 8 are 20 to 34 years old (4 male, 4 female), 8 are 35 to 49 years old (4 male, 4 female), and 8 are 50 to 64 years old (4 male, 4 female). He then measured the time (in minutes) required to complete a certain task. The data obtained are shown next. (a) The learning times are approximately normally distributed. Verify the requirement of equal population variances. (b) Determine whether there is significant interaction between age and gender. (c) If there is no significant interaction, determine whether there is significant difference in the means for the three age groups. (d) Draw an interaction plot of the data to support the results of parts (b) and (c). (e) If there is significant difference in the means for the three age groups, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05.

The following table summarizes the sample mean earnings, in thousands of dollars, of a random sample of yearround, full-time workers by gender and age. (a) Construct an interaction plot for the data. (b) Does the interaction plot indicate a significant interaction effect? Explain? (c) What, if anything, can you conclude about the significance of the main effects?