APPENDIX D 805 of the car does not appear to have an effect on the force on the femur of the left leg in crash tests. 7. Test statistic: F = 28.1666. P@value 6 0.0001. Reject H0: m1 = m2 = m3. There is sufficient evidence to warrant rejection of the claim that the three different types of Chips Ahoy cookies have the same mean number of chocolate chips. 9. Test statistic: F = 9.4695. P-value: 0.001. Reject H0: m1 = m2 = m3. There is sufficient evidence to warrant rejection of the claim that pages from books by Clancy, Rowling, and Tolstoy have the same mean Flesch Reading Ease score. It appears that at least one of the authors has a mean Flesch Reading Ease score that is different from the others. With means of 70.73, 80.75, and 66.15, it appears that Rowling is different by having the highest Flesch Reading Ease score, but ANOVA does not justify a conclusion that any particular mean is different from the others. 11. Test statistic: F = 27.2474. P-value: 0.000. Reject H0: m1 = m2 = m3. There is sufficient evidence to warrant rejection of the claim that the three different miles have the same mean time. These data suggest that the third mile appears to take longer, and a reasonable explanation is that the third mile has a hill. 13. Test statistic: F = 0.0558. P-value: 0.946. Fail to reject H0: m1 = m2 = m3. There is not sufficient evidence to warrant rejection of the claim that the three vehicle size categories (midsize, large, SUV) have the same mean head injury criterion (HIC) measurements in crash tests. For midsize, large, and SUV cars, size category of the car does not appear to have an effect on the HIC measurements. 15. Test statistic: F = 144.4462. P-value: 0.000. Reject H0: m1 = m2 = m3 = m4. There is sufficient evidence to warrant rejection of the claim that the four rides have the same mean wait time. At least one of the rides has a mean 10 AM wait time that is different from the others. 17. The Tukey test results show different P-values, but they are not dramatically different. The Tukey results suggest the same conclusions as the Bonferroni test. Section 12-2 1. The measurements are categorized using two different factors of (1) femur side (left, right) and (2) vehicle size (small, midsize, large, SUV). 3. a. An interaction between two factors or variables occurs if the effect of one of the factors changes for different categories of the other factor. b. If there is an interaction effect, we should not proceed with individual tests for effects from the row factor and column factor. If there is an interaction, we should not consider the effects of one factor without considering the effects of the other factor. c. The lines are not too far from being parallel except for the mean for the left femur in small cars. That large difference does suggest that there is an interaction effect between femur side and size of vehicle. 5. For interaction, the test statistic is F = 4.4313 and the P-value is 0.0103, so there is sufficient evidence to warrant rejection of the null hypothesis of no interaction effect. Because there appears to be an interaction between femur side (left, right) and vehicle size category, we should not proceed with a test for an effect from c. (1) Using correlation: r = -0.481, P@value = 0.412 (Table: 70.05), critical values: r = {0.878 (assuming a 0.05 significance level). There is not sufficient evidence to support a claim of a correlation. (2) Test statistic: t = -0.459, P@value = 0.670 (Table: 70.20), critical values: t = {2.776 (assuming a 0.05 significance level). There is not sufficient evidence to support a claim of a difference between the scores of the siblings. 2. a. Are the last digits from a population in which they all occur with the same frequency? b. Use the goodness-of-fit test, as in Section 11-1. c. Test statistic: x2 = 6.500. P@value = 0.689 (Table: 70.10). Critical value: x2 = 16.919 (assuming a 0.05 significance level). Fail to reject the null hypothesis that the last digits are from a population in which they all occur with the same frequency. 3. a. Is there a significant difference between the distances run by males and the distances run by females? b. Use the test for a difference between the means of two independent populations, as in Section 9-2. c. H0: m1 = m2. H1: m1 ≠ m2. Test statistic: t = -0.536. P@value = 0.613 (Table: P@value 70.20). Critical values (assuming a 0.05 significance level): t = {2.492 (Table: {2.776). Fail to reject the null hypothesis of no difference. There is not sufficient evidence to reject the claim of no significant difference between the distances run by males and females. (The same conclusion results from a 95% confidence interval: -6.8 miles 6m1 - m2 64.4 miles.) 4. a. Are the variables of workday and shift independent? b. Use the x2 test for a contingency table, as in Section 11-2. c. Test statistic: x2 = 4.225. P@value = 0.376 (Table: 70.10). Critical value: x2 = 9.488 (assuming a 0.05 significance level). There is not sufficient evidence to warrant rejection of the claim of independence between shift and day of the week. 5. Test statistic: x2 =3.409. P-value = 0.0648 (Table: 70.05). Critical value: x2 = 3.841. There is not sufficient evidence to warrant rejection of the claim that the form of the 100-yuan gift is independent of whether the money was spent. There is not sufficient evidence to support the claim of a denomination effect. Women in China do not appear to be affected by whether 100 yuan are in the form of a single bill or several smaller bills. 6. a. 128>150 = 0.853 b. 143>150 = 0.953 c. 0.727 (not 0.728) Chapter 12 Answers Section 12-1 1. a. The chest compression amounts are categorized according to the one characteristic of vehicle size category. b. The terminology of analysis of variance refers to the method used to test for equality of the four population means. That method is based on two different estimates of a common population variance. 3. The test statistic is F = 3.815, and the F distribution applies. 5. Test statistic: F = 0.57. P-value: 0.638. Fail to reject H0: m1 = m2 = m3 = m4. There is not sufficient evidence to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests. Size
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