562 CHAPTER 10 Chi-Square Tests and the F-Distribution Using MSB ≈ 10.9616 and MSW = 7.3, the test statistic is F = MSB MSW ≈ 10.9616 7.3 ≈ 1.50. The figure shows the location of the rejection region and the test statistic F. Because F is not in the rejection region, you fail to reject the null hypothesis. Interpretation There is not enough evidence at the 1% level of significance to conclude that there is a difference in the mean length of time it takes the three pain relievers to provide relief from headache pain. The ANOVA summary table for Example 1 is shown below. Variation Sum of squares Degrees of freedom Mean squares F Between 21.9232 2 10.9616 1.50 Within 73 10 7.3 TRY IT YOURSELF 1 A sales analyst wants to determine whether there is a difference in the mean monthly sales of a company’s four sales regions. Several salespersons from each region are randomly selected and they provide their sales amounts (in thousands of dollars) for the previous month. The results are shown in the table. At a = 0.05, can the analyst conclude that there is a difference in the mean monthly sales among the sales regions? Assume that each population of sales is normally distributed and that the population variances are equal. North East South West 34 47 40 21 28 36 30 30 18 30 41 24 24 38 29 37 44 23 n1 = 4 n2 = 5 n3 = 4 n4 = 5 x1 = 26 x2 = 39 x3 = 35 x4 = 27 s2 1 ≈ 45.33 s 2 2 = 45 s 2 3 ≈ 40.67 s 2 4 = 42.5 Answer: Page A43 Using technology greatly simplifies the one-way ANOVA process. When using technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to perform a one-way analysis of variance test, you can use P@values to decide whether to reject the null hypothesis. If the P@value is less than a, then reject H0. 2 4 6 8 F F0 = 7.56 F≈ 1.50 α= 0.01 Picturing the World A researcher wants to determine whether there is a difference in the mean lengths of time wasted at work for people in California, Georgia, and Pennsylvania. Several people from each state who work 8-hour days are randomly selected and they are asked to estimate how much time (in hours) they waste at work each day.The results are shown in the table. (Adapted from Salary.com) CA GA PA 2 2 1.75 1.75 2.5 3 2.5 1.25 2.75 3 2.25 2 2.75 1.5 3 3.25 3 2.5 1.25 2.75 2.75 2 2.25 3.25 2.5 2 3 1.75 1 2.75 1.5 2.25 2.25 At A = 0.10, can the researcher conclude that there is a difference in the mean lengths of time wasted at work among the states? Assume that each population is normally distributed and that the population variances are equal.
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