Of the 98 teachers who responded, 23.5% said that they had one or more tattoos.

a. Construct and interpret a 95% confidence interval for the true proportion of all teachers at the AP® institute who would say they have tattoos.

b. Does the interval in part (a) provide convincing evidence that the proportion of all teachers at the institute who would say they have tattoos is different from 0.29 (the value cited in the Harris Poll report)? Justify your answer.

c. Two of the selected teachers refused to respond to the survey. If both of these teachers had responded, could your answer to part (b) have changed? Justify your answer.

About 1100 high school teachers attended a weeklong summer institute for teaching AP® Statistics classes. After learning of the survey described in Exercise 56, the teachers in the AP® Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted to take a random sample of 100 teachers at the institute. One of the questions on the survey was: Do you have any tattoos on your body?

(Circle one)  YES  NO

Exercise 56.

What percent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302 adults and found 29% of respondents had at least 1 tattoo. According to the published report, “Respondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.” Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.