Question

While reviewing the sample of audit​ fees, a senior accountant for the firm notes that the fee charged by the​ firm's accountants depends on the complexity of the return. A comparison of actual charges therefore might not provide the information needed to set next​ year's fees. To better understand the fee​ structure, the senior accountant requests a new sample that measures the time the accountants spent on the audit. Last​ year, the average hours charged per client audit was 2.97 hours. A new sample of 15 audit times shows the following times in hours.

2.5, 4.7, 3.8, 3.2, 3.3
2.8, 4.9, 4.5, 3.6, 4.8
3.2, 2.7, 3.6, 4.8, 4.6

a) Assume the conditions necessary for inference are met. Find a 95​% confidence interval for the mean audit time

The

9595​%

confidence interval to estimate the mean audit time is from __ to __

Answer 1

Sol:

alpha=1-0.95=0.05

alpha/2=0.05/2=0.025

df=n-1=15-1=14

t critical in excel ==T.INV(0.025,14)=2.14479

sample mean=xbar=3.8

sample sd=s=0.8493695

95% confidence interval for mean is

xbar-t*s/qrt(n),xbar+t*s/sqrt(n)

3.8-2.14479*0.8493695/sqrt(15),3.8+2.14479*0.8493695/sqrt(15

3.329634,4.270366

95% lower limit for mean= 3.329634

95% upper limit for mean=4.270366

95% confidence interval to estimate the mean audit time is from 3.33 to 4.27

(I HAVE ROUNDED TO 2 DECIMALS)