It probably wouldn’t surprise you to know that Valentine’s Day means big business for florists, jewelry stores, and restaurants. But would it surprise you to know that it is also a big day for pet stores? In January 2010, the National Retail Federation conducted a survey of consumers who they believed were selected in a way that would produce a sample representative of the population of adults in the United States (“This Valentine’s Day, Couples Cut Back on Gifts to Each Other, According to NRF Survey,” www.nrf.com). One of the questions in the survey asked if the respondent planned to spend money on a Valentine’s Day gift for his or her pet this year.
a. The proportion who responded that they did plan to purchase a gift for their pet was .173. Suppose that the sample size for this survey was n = 200. Construct and interpret a 95% confidence interval for the proportion of all U.S. adults who planned to purchase a Valentine’s Day gift for their pet in 2010.
b. The actual sample size for the survey was much larger than 200. Would a 95% confidence interval computed using the actual sample size have been narrower or wider than the confidence interval computed in Part (a)?
c. Still assuming a sample size of n = 200, carry out a hypothesis test to determine if the data provides convincing evidence that the proportion who planned to buy a Valentine’s Day gift for their pet in 2010 was greater than .15. Use a significance level of .05.