Chapter 7, Problem 75SE

Democratic (Examples 15, 16, 17, 18) Voters and the FBI In 2003 and 2017 Gallup asked Democratic voters about their views on the FBI. In 2003, $44\%$ thought the FBI did a good or excellent job. In 2017, $69\%$ of Democratic voters felt this way. Assume these percentages are based on samples of 1200 Democratic voters.

a. Can we conclude, on the basis of these two percentages alone, that the proportion of Democratic voters who think the FBI is doing a good or excellent job has increase from 2003 to 2017? Why or why not?

b. Check that the conditions for using a two-proportion confidence interval hold. You can assume that the sample is a random sample.

c. Construct a $95\%$ confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent job, $p_1-p_2$. Let $p_1$ be the proportion of Democratic voters who felt this way in 2003 and $p_2$ be the proportion of Democratic voters who felt this way in 2017.

d. Interpret the interval you constructed in part

c. Has the proportion of Democratic voters who feel this way increased? Explain.