A report on the politics of climate summarized data from a survey on public opinion of renewable and other energy sources. It was reported that 55% of the people in a sample from western states said that they have considered installing solar panels on their homes. This percentage was based on a representative sample of 364 homeowners in the western United States.

The report also indicated that 35% of those in a representative sample of 532 homeowners in southern states said that they had considered installing solar panels.

(a)

Use the given information to construct a 90% confidence interval for the proportion of all homeowners in the southern states who have considered installing solar panels. (Round your answers to three decimal places.)

We are 90% confident that the true proportion of all homeowners in the southern states who have considered installing solar panels falls directly in the middle of this interval. We are 90% confident that the true proportion of all homeowners in the southern states who have considered installing solar panels falls within this interval. There is a 90% chance that the true proportion of all homeowners in the southern states who have considered installing solar panels falls directly in the middle of this interval. We are 90% confident that the mean number of all homeowners in the southern states who have considered installing solar panels falls within this interval. There is a 90% chance that the true proportion of all homeowners in the southern states who have considered installing solar panels falls within this interval.

(b)

Give two reasons why the confidence interval in part (a) is narrower than a 90% confidence interval for the proportion of all homeowners in western states who have considered installing solar panels. (Select all that apply.)

The confidence interval in part (a) is narrower because the confidence level for southern states is higher than the confidence level for western states. The confidence interval in part (a) is narrower because the sample size for southern states is larger than the sample size for western states. The confidence interval in part (a) is narrower because the sample proportion for southern states is closer to 0.5 than the sample proportion for western states. The confidence interval in part (a) is narrower because the sample proportion for southern states is farther from 0.5 than the sample proportion for western states. The confidence interval in part (a) is narrower because the confidence level for southern states is lower than the confidence level for western states. The confidence interval in part (a) is narrower because the sample size for southern states is smaller than the sample size for western states.