In 2018 Gallup reported that 52% of Americans are dissatisfied with the quality of the environment in the United States. This was based on a 95% confidence interval with a margin of error of 4 percentage points. Assume the conditions for constructing the confidence interval are met.

a. Report and interpret the confidence interval for the population proportion that are dissatisfied with the quality of the environment in the United States in 2018.

b. If the sample size were larger and the sample proportion stayed the same, would the resulting interval be wider or narrower than the one obtained in part a?

c. If the confidence level were 90% rather than 95% and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a?

d. In 2018 the population of the United States was roughly 327 million. If the population had been half that size, would this have changed any of the confidence intervals constructed in this problem? In other words, if the conditions for constructing a confidence interval are met, does the population size have any effect on the width of the interval?