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 ________ 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?

Answer 1

(Since there are more than 4 parts i will answer first 4)

Given :

actual mean = 47

actual SD = 9

sample size = 70

a.

answer : 44.229 db , 49.771 db

b.

margin of error = z*sd/(n^0.5) = 1.645*9/(70^0.5) = 1.77 db

answer : We can be 90% confident that the actual mean noise level in hospitals is _47_ db with a margin of error of _1.77_ db.

c.

here we will take sample size = 81

we want 100%-2% = 98% confidence interval

answer : Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between _44.498 db and _49.502_ db.

d.

answer : A 99.9% confidence interval for the actual mean noise level in hospitals is _43.46_ db , _50.54_ db .

P.S. (please upvote if you find the answer satisfactory)