Verbal IQ Scores Example in this section used performance

Problem 1BSC Two-Way ANOVA? Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is ?two-way? analysis of variance? That is, what is “two-way” about the data entered in the table?

Problem 1CQQ Measures of Voltage The author measured voltage amounts from three different sources: (1) electricity supplied directly to the author’s home, (2) an independent gas-powered Generac generator (model PP 5000), and (3) an uninterruptible power supply (APC model CS 350) connected to the author’s home power supply. The results from analysis of variance are shown below. What is the null hypothesis for this analysis of variance test? What specific result is used in deciding to reject ?H0? or fail to reject ?H0?? Based on the displayed results, should you reject ?H0? or fail to reject ?H0??

Problem 1CRE Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Descriptive Statistics? Include appropriate units in all answers. a.? Find the mean for each of the three groups. b.? Find the standard deviation for each of the three groups. c.? Find the variance for each of the three groups. d.? What is the level of measurement of the data (nominal, ordinal, interval, ratio)?

Problem 1RE Car Weight and Fuel Consumption? Data Set 14 in Appendix B includes highway fuel consumption amounts for cars with 4 cylinders, 6 cylinders, and 8 cylinders. (The 5-cylinder Volvo S60 is excluded from this exercise.) Analysis of variance is used with the highway fuel consumption amounts (mi/gal) categorized according to the number of cylinders (4, 6, 8); the results are shown in the following display. Identify the null hypothesis, test statistic, and ?P?-value, and state the final conclusion in nontechnical terms.

Problem 2BSC Two-Way ANOVA? If we have a goal of using the data described in Exercise to (1)determine whether size of a dir has an effect on the load measurements and (2) to determine whether the location of the femur (left or right) has an effect on the load measurements, should we use one-way analysis of variance for the two individual tests? Why or why not? Exercise Two-Way ANOVA? Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is ?two-way? analysis of variance? That is, what is “two-way” about the data entered in the table?

Problem 2CQQ Based on the conclusion from Exercise, can electrical appliances be expected to behave the same way when run from the three different power sources? Why or why not? Exercise Measures of Voltage? The author measured voltage amounts from three different sources: (1) electricity supplied directly to the author’s home, (2) an independent gas-powered Generac generator (model PP 5000), and (3) an uninterruptible power supply (APC model CS 350) connected to the author’s home power supply. The results from analysis of variance are shown below. What is the null hypothesis for this analysis of variance test? What specific result is used in deciding to reject ?H0? or fail to reject ?H0?? Based on the displayed results, should you reject ?H0? or fail to reject ?H0??

Problem 2CRE Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Comparing Two Means? Treating the data as samples from larger populations, test the claim that there is a difference between the mean for presidents and the mean for British monarchs.

Problem 3BSC InteractionWhat is an interaction between two factors? In general, when using two-way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?

Problem 2RE Poplar Tree Experiment? Weights (kg) of poplar trees were obtained from trees planted in one region that was rich and moist and a second region that was sandy and dry. The trees were given different treatments as identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc.; the Minitab results are displayed. What do you conclude?

Problem 3CQQ For the analysis of variance test described in Exercise, is that test left-tailed, right-tailed, or two-tailed? Exercise Measures of Voltage? The author measured voltage amounts from three different sources: (1) electricity supplied directly to the author’s home, (2) an independent gas-powered Generac generator (model PP 5000), and (3) an uninterruptible power supply (APC model CS 350) connected to the author’s home power supply. The results from analysis of variance are shown below. What is the null hypothesis for this analysis of variance test? What specific result is used in deciding to reject ?H0? or fail to reject ?H0?? Based on the displayed results, should you reject ?H0? or fail to reject ?H0??

Problem 3CRE Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Normality Assessment? Use the longevity times for presidents and determine whether they appear to come from a population having a normal distribution. Explain why the distribution does or does not appear to be normal.

Problem 4BSC Balanced Design?Does the table given in Exercise constitute a ?balanced design?? Why or why not? Exercise Two-Way ANOVA? Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is ?two-way? analysis of variance? That is, what is “two-way” about the data entered in the table?

Problem 4CQQ Identify the value of the test statistic in the display included with Exercise. In general, do larger test statistics result in larger T-values, smaller P-values, or P-values that are unrelated to the value of the test statistic? Exercise Measures of Voltage? The author measured voltage amounts from three different sources: (1) electricity supplied directly to the author’s home, (2) an independent gas-powered Generac generator (model PP 5000), and (3) an uninterruptible power supply (APC model CS 350) connected to the author’s home power supply. The results from analysis of variance are shown below. What is the null hypothesis for this analysis of variance test? What specific result is used in deciding to reject ?H0? or fail to reject ?H0?? Based on the displayed results, should you reject ?H0? or fail to reject ?H0??

Problem 4CRE Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Confidence Interval? Use the longevity times for presidents and construct a 95% confidence interval estimate of the population mean.

Problem 5BSC Car Crash Tests? If we use the data described in Exercise with two-way analysis of variance, we get the accompanying display. What do you conclude? Exercise Two-Way ANOVA? Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is ?two-way? analysis of variance? That is, what is “two-way” about the data entered in the table?

Problem 5CRE Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. ANOVA?The display below results from using the one-way analysis of variance test. a.? What is the null hypothesis? b.? Assuming a 0.05 significance level, what conclusion is indicated by the displayed results?

Problem 6CQQ In general, what is one-way analysis of variance used for?

Problem 6BSC Car Crash Tests? The following table lists results from car crash tests. The listed values are measures of chest deceleration (in g) categorized by type (whether the car is foreign or domestic) and car size (small, midsize, large). Results from two-way analysis of variance are also displayed. Use the displayed results and use a 0.05 significance level. What do you conclude?

Problem 7BSC Verbal IQ Scores? Example in this section used ?performance? IQ scores from Data Set 5 in Appendix B for two-way analysis of variance with the factors of sex (male, female) and measured blood lead level (low, medium, high). If we use the verbal? IQ scores with those same factors, we get the accompanying results. Use the displayed results and use a 0.05 significance level. What do you conclude? Example

Problem 7CQQ What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

For the analysis of variance test described in Exercise 1, is that test left­tailed, right­tailed, or two­tailed?

Statistical Literacy and Critical Thinking Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not?

Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P­-values, smaller P-values, or P­-values that are unrelated to the value of the test statistic?

Please be aware that some of the following problems may require knowledge of concepts presented in previous chapters. In Exercises 1­5, refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Lottery: Goodness­of­Fit The bars in the histogram included with Exercise 9 depict these frequencies: 21, 19, 15, 18, 24, 18, 16, 24, 30, and 15. Test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?

Car Weight and Fuel Consumption Data Set 14 in Appendix B includes highway fuel consumption amounts for cars with 4 cylinders, 6 cylinders, and 8 cylinders. (The 5­cylinder Volvo S60 is excluded from this exercise.) Analysis of variance is used with the highway fuel consumption amounts (mi/gal) categorized according to the number of cylinders (4, 6, 8); the results are shown in the following display. Identify the null hypothesis, test statistic, and P­-value, and state the final conlusion in nontechnical terms. MINITAB

Statistical Literacy and Critical Thinking Two­Way ANOVA If we have a goal of using the data described in Exercise 1 to (1) determine whether size of a car has an effect on the load measurements and (2) to determine whether the location of the femur (left or right) has an effect on the load measurements, should we use one-­way analysis of variance for the two individual tests? Why or why not?

Based on the conclusion from Exercise 1, can electrical appliances be expected to behave the same way when run from the three different power sources? Why or why not?

Given below is a Minitab display resulting from two-­way analysis of variance with sample data consisting of 18 different student estimates of the length of a classroom. The values are categorized according to sex and major (math, business, liberal arts). What do you conclude about an interaction between sex and major? MINITAB

Statistical Literacy and Critical Thinking Self­Esteem The following table lists measures of self-­esteem obtained from a student project as supervised by Jannay Morrow at Vassar College (based on data from Richard Lowry). The objective of the project was to study how levels of self­-esteem in subjects relate to their perceptions of self-esteem in other target people who were described in writing. Self-­esteem levels were measured using the Coopersmith Self­Esteem Inventory, and the test here works well even though the data are at the ordinal level of measurement. Use a 0.05 significance level and apply the methods of two-­way analysis of variance. What do you conclude?

Using the same results given in Exercise 8, does it appear that the length estimates are affected by the sex of the subject?

In Exercises 1-­5, refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Comparing Two Means Treating the data as samples from larger populations, test the claim that there is a difference between the mean for presidents and the mean for British monarchs.

Poplar Tree Experiment Weights (kg) of poplar trees were obtained from trees planted in one region that was rich and moist and a second region that was sandy and dry. The trees were given different treatments as identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc.; the Minitab results are displayed. What do you conclude?

Problem 3BSC InteractionWhat is an interaction between two factors? In general, when using two-way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?

Lottery: Interpreting a Graph Shown below is a histogram of digits selected in California's Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive. a. If the lottery works correctly, what should be the shape of the histogram in the long run? Does the histogram shown here depict the expected distribution? b. Does the display depict a normal distribution? Why or why not?

Statistical Literacy and Critical Thinking Pulse Rate The following table lists pulse rates obtained from Data Set 1 in Appendix B. Use a 0.05 significance level and apply the methods of two-­way analysis of variance. What do you conclude?

Using the same results given in Exercise 8, does it appear that the length estimates are affected by the subject's major?

In Exercises 1-­5, refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Confidence Interval Use the longevity times for presidents and construct a 95% confidence interval estimate of the population mean.

Smoking, Body Temperature, Gender The table below lists body temperatures obtained from randomly selected subjects (based on Data Set 3 in Appendix B). The temperatures are categorized according to gender and whether the subject smokes. Using a 0.05 significance level, test for an interaction between gender and smoking, test for an effect from gender, and test for an effect from smoking. What do you conclude?

Car Crash Tests If we use the data described in Exercise 1 with two-­way analysis of variance, we get the accompanying display. What do you conclude? MINITAB

Two-­Way ANOVA Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is two-­way analysis of variance? That is, what is “two­-way” about the data entered in the table?

Measures of Voltage The author measured voltage amounts from three different sources: (1) electricity supplied directly to the author's home, (2) an independent gas-­powered Generac generator (model PP 5000), and (3) an uninterruptible power supply (APC model CS 350) connected to the author's home power supply. The results from analysis of variance are shown below. What is the null hypothesis for this analysis of variance test? What specific result is used in deciding to reject H 0 or fail to reject H 0 ? Based on the displayed results, should you reject H 0 or fail to reject H 0 ? MINITAB

In Exercises 1-­5, refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Descriptive Statistics Include appropriate units in all answers. a. Find the mean for each of the three groups. b. Find the standard deviation for each of the three groups. c. Find the variance for each of the three groups. d. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?

Verbal IQ Scores Example 1 in this section used performance IQ scores from Data Set 5 in Appendix B for two­-way analysis of variance with the factors of sex (male, female) and measured blood lead level (low, medium, high). If we use the verbal IQ scores with those same factors, we get the accompanying results. Use the displayed results and use a 0.05 significance level. What do you conclude? MINITAB

Problem 7CQQ What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

Pancake Experiment Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from two­-way analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude? MINITAB

In Exercises 1-­5, refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. ANOVA The display below results from using the one­-way analysis of variance test. a. What is the null hypothesis? b. Assuming a 0.05 significance level, what conclusion is indicated by the displayed results? MINITAB

Car Crash Tests The following table lists results from car crash tests. The listed values are measures of chest deceleration (in g) categorized by type (whether the car is foreign or domestic) and car size (small, midsize, large). Results from two­-way analysis of variance are also displayed. Use the displayed results and use a 0.05 significance level. What do you conclude? MINITAB

Problem 6CQQ In general, what is one-way analysis of variance used for?