Online insurance III Exercises 17 and 19 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.
Exercise 17
Revealing information Eight hundred eight-six randomly sampled teens were asked which of several personal items of information they thought it okay to share with someone they had just met. Forty-four percent said it was okay to share their e-mail addresses, but only 29% said they would give out their cell phone numbers. A researcher claims that a two- proportion z-test could tell whether there was a real difference among all teens. Explain why that test would not be appropriate for these data.
Exercise 19
Gender gap A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can’t know this, but suppose the candidate has a positive image with 59% of males but with only 53% of females.
a) What kind of sampling design is his staff planning to use?
b) What difference would you expect the poll to show?
c) Of course, sampling error means the poll won’t reflect the difference perfectly. What’s the standard deviation for the difference in the proportions?
d) Sketch a sampling model for the size difference in proportions of men and women with favorable impressions of this candidate that might appear in a poll like this.
e) Could the campaign be misled by the poll, concluding that there really is no gender gap? Explain.