The ideal (daytime) noise-level for hospitals is 45 decibels with a standard dev

Question

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)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.

(b) 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.

Explanation / Answer

CI is mean-z(a/2)*s/sqrt(n) to mean+z(a/2)*s/sqrt(n)

so,

a)

Z for 99% = Z(0.01/2) = Z(0.005) = 2.58

so,

CI = ( 47-2.58*10/sqrt(81) , 47+2.58*10/sqrt(81)) = (44.13 , 49.87)

b)

We can be 90% confident that the actual mean noise level in hospitals is 47 db , db with a margin of error of 1.83 db

c)

here we are asked to calculate 98% CI

z for 98% CI = 2.33

so,

CI = ( 47-2.33*10/sqrt(81) , 47+2.33*10/sqrt(81)) = (44.41 , 49.59)

d)

correct

e)

most typical means we are asked to calculate 95% CI

Z for 95% CI = 1.96

==> CI = ( 47-1.96*10/sqrt(81) , 47+1.96*10/sqrt(81)) = (44.82 , 49.18)

f)

We are 95% confident that the actual mean noise level in hospitals is 47 db with a margin of error of 2.18 db

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