Question

The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 9 db; which is to say, this may not be true. A simple random sample of 70 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 9 db. All answers to two places after the decimal.

(a) A 99% confidence interval for the actual mean noise level in hospitals is

(b) We can be 90% confident that the actual mean noise level in hospitals is

(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?

Answer 1