In a recent USA Today poll, most customers shopping online indicated that shipping options are important when making buying decisions.18 There are often several shipping options for online consumers,...

In a recent USA Today poll, most customers shopping online indicated that shipping options are important when making buying decisions.18 There are often several shipping options for online consumers, including overnight delivery, 3-day ground service, and free slow shipping. Suppose that, in a random sample of 500 adults in California, 135 said they prefer free slow shipping. In a random sample of 600 adults in New Jersey, 204 indicated they prefer free slow shipping.

a. Conduct a hypothesis test concerning two population proportions to determine whether there is any evidence that the proportion of adults who prefer free slow shipping is different in California and in New Jersey. Find the p value associated with this test.

 b. Consider “California’’ and “New Jersey’’ as populations and “prefer’’ and “not preferred’’ as categories. Using the data given in this problem, construct a two-way frequency table and conduct a test for homogeneity of populations. Use technology to find the p value for this test.

c. What is the relationship between the value of the test statistic in part (a) and the value of the test statistic in part (b)? How are the p values related? Why do these relationships make sense?