Question

The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 12 db; which is to say, this may not be true. A simple random sample of 75 hospitals at a moment during the day gives a mean noise level of 47 db. Assume that the standard deviation of noise level for all hospitals is really 12 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 0.5 db?  

(h) How many hospitals must we examine to have 99.9% confidence that we have the margin of error to within 0.5 db?

Answer 1