(AP Statistics, Periods D and F)

Mr. Hansen's tests are carefully constructed so as to have a standard deviation of 10 points. (Actually, it's somewhat unrealistic that we could know this, but let's work with it.)

(a) If we administer the test to an SRS of 20 St. Albans students, who score an average of 82.3% on the test, what is a 90% confidence interval for the "true" population average score on the test?

(b) How many students would we need in our SRS so that an interval having the same width as the interval you calculated in part (a) would constitute a 95% confidence interval?

(c) If, when the test is administered to that larger SRS, the mean score is 84.1%, what is the new estimate of the population average score (with 95% confidence)?