The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 10 db. A simple random sample of 81 hospitals at a moment during the day gives a mean noise level of 47 db. Assume that the standard deviation of noise level is really 10 db. All answers to two places after the decimal.
(a) A 99% confidence interval for the actual mean noise level in hospitals is ( db, db).
(b) We can be 90% confident that the actual mean noise level in hospitals is db with a margin of error of db.
(c) Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between db and db.
(d) A 99.9% confidence interval for the actual mean noise level in hospitals is ( db, db).
(e) Assuming our sample of hospitals is among the most typical half of such samples, the actual mean noise level in hospitals is between db and db.
(f) We are 95% confident that the actual mean noise level in hospitals is db, with a margin of error of db.
(g) How many hospitals must we examine to have 95% confidence that we have the margin of error to within 1 db?
(h) How many hospitals must we examine to have 99.9% confidence that we have the margin of error to within 1 db?