In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Quality Family Time? The accompanying STATDISK display shows results from the claim and data given in Exercise 1. Test that claim. Exercise 1 Quality Family Time? The table below lists days of the week selected by a random sample of 1005 subjects who were asked to identify the day of the week that is best for quality family time (based on results from a Pillsbury survey reported in ?USA Today).? Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. If we test that claim using the goodness-of-fit test described in this section, what is it that we actually test?

Solution 5BSC S M F S Th u o Tues Wed r a urs n n i t 5 3 2 4 2 9 19 11 8 0 1 3 2 Answer: Step 1 Given, days of the week selected by a random sample of 1005 subjects who were asked to identify the day of the week that is best for quality family time. Here, we need to consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. The Hypotheses can be expressed as H0 The days of the week are selected with a uniform distribution. H : The days of the week are not selected with a uniform distribution. 1 From STATDISK output, we see that = 1934.97 is the required test statistic value. Therefore, the Critical Value for = 12.592 with 6 degrees of freedom, since level of significance is not given let us assume at 5% level of significance. 2 2 Here, the calculated test statistic value = 1934.97 is greater than the critical value = 12.592, we reject the null hypothesis at 5% level of significance. Hence we conclude that there is no sufficient evidence to support the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected.