Chapter 7, Problem 76SE

Trust in Judiciary In 2016 and 2017 Gallup asked American adults about their amount of trust they had in the judicial branch of government. In 2016, $61\%$ expressed a fair amount or great deal of trust in the judiciary. In 2017, $68\%$ of Americans felt this way. These percentages are based on samples of 1022 American adults.

a. Explain why it would be inappropriate to conclude, based on these percentages alone, that the percentage of Americans who had a fair amount or great deal of trust in the judicial branch of government increased from 2016 to 2017.

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 Americans who expressed this level of trust in the judiciary, $p_1-p_2$, where $p_1$ is the 2016 population proportion and $p_2$ is the 2017 population proportion.

d. Based on the confidence interval constructed in part c, can we conclude that proportion of Americans with this level of trust in the judiciary increased from 2016 to 2017? Explain.