Chapter 13, Problem 34SE

Soda Does soda constitute a larger part of the diet for women than it does for men? A StatCrunch survey asked people to report the percentage of their liquid intake that is soda. The sample mean for the 169 females was 19.51%, and the sample mean for the 163 males was 17.74% To determine whether the mean for all women StatCrunch users was more than the mean for all men, we performed a randomization test.

a. The histogram shows the results of 1000 randomizations of the data. In each randomization, 169 observations from the merged “men” and “women” values were randomly determined to be from “women” and the rest from “men.” We calculated the mean difference in the percentage of sodas between these randomly determined groups. Note that the distribution is centered at about 0, because the randomization forces the null hypothesis to be true. The red line shows the observed sample mean percentage of soda for the women minus the mean percentage of soda for the men. From the graph, does it look like the observed mean difference is unusual for this data set? Explain.

b. The software output estimates the probability of having an observed difference of 1.77 or more. (See the column labeled “Proportion $=>$ Observed”). Where does the value of 1.77 come from?

c. Report the $p$ -value for the one-sided alternative that the mean for the women is greater than the mean for the men.

d. Using a significance level of 0.05, can we reject the null hypothesis that the means are equal and so conclude that these women StatCrunch users tend to report a higher soda intake percentage than these men? (Assume the sample was randomly selected

e. from the population.)

(Source: StatCrunch survey results. Owner: scsurvey)