In a simple random sample of 1500 young Americans, 87% had earned a high school diploma.

a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?

b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.

c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.

d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who earn high school diplomas has increased? Explain.