636 CHAPTER 12 Analysis of Variance 10.Smoking, Gender, and Body Temperature The table below lists body temperatures obtained from randomly selected subjects (based on Data Set 5 “Body Temperatures” in Appendix B). 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? Smokes Does not smoke Male 98.8 97.6 98.0 98.5 98.4 97.8 98.0 97.0 Female 98.0 98.5 98.3 98.7 97.7 98.0 98.2 99.1 11.Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3 on page 627. How are the results affected in each of the following cases? a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged. d. The first sample value in the first cell is changed so that it becomes an outlier. 12-2 Beyond the Basics 1.Cola Weights Data Set 37 “Cola Weights and Volumes” in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) Diet Coke, (3) regular Pepsi, and (4) Diet Pepsi. The results from analysis of variance are shown in the Minitab display below. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H0? What do you conclude about equality of the mean weights from the four samples? Chapter Quick Quiz Minitab 2.Cola Weights For the four samples described in Exercise 1, the sample of regular Coke has a mean weight of 0.81682 lb, the sample of Diet Coke has a mean weight of 0.78479 lb, the sample of regular Pepsi has a mean weight of 0.82410 lb, and the sample of Diet Pepsi has a mean weight of 0.78386 lb. If we use analysis of variance and reach a conclusion to reject equality of the four sample means, can we then conclude that any of the specific samples have means that are significantly different from the others? 3. Cola Weights For the analysis of variance test described in Exercise 1, is that test left-tailed, right-tailed, or two-tailed? 4.Cola Weights 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? 5. Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance? 6.One-Way ANOVA In general, what is one-way analysis of variance used for?
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