Chapter 10, Problem 29PS

An online survey asked 1,004 adults “if purchasing a used car made certain upgrades or features more affordable, what would be preferred luxury upgrade?� The results indicated that $9\%$ of the males and $14\%$ of the females answered window tinting.

The sample sizes of males and females were not provided. Suppose that both sample sizes were 502 and that 46 of 502 males and 71 of 502 reported window tinting as their preferred luxury upgrade of choice.

a. Is there evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.01 level of significance?

b. Find the p-value in (a) and interpret its meaning.

c. Construct and interpret a $99\%$ confidence interval estimate for the difference between the proportion of males and females who said they prefer window tinting as a luxury upgrade.

d. What are your answers to (a) through (c) If 60 males said they prefer window tinting as a luxury upgrade?