Question

Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advices and support from the accountant if the client were audited. A large accounting firm is trying to determine what fee to charge for next​ year's returns. In previous​ years, the actual mean cost to the firm for attending a client audit session was ​$650. To determine if this cost has​ changed, the firm randomly samples 35 client audit fees. The sample mean audit cost was ​$670 with a standard deviation of ​$85. Complete parts a and b below. ​

a) Develop a 90​% confidence interval estimate for the mean audit cost.

The 90​% confidence interval for the mean audit cost is __ to __

(Round to the nearest dollar as​ needed.)

​b) Based on your confidence​ interval, what do you think of the claim that the mean cost has​ changed?

A. The interval contains the historical mean ​$650​, which does not support the claim that the mean cost has changed.

B. The interval does not contain the historical mean ​$650​, which supports claim that the mean cost has changed.

C. The interval contains the historical mean ​$650​, which supports the claim that the mean cost has changed.

D. The interval does not contain the historical mean ​$650​, which does not support the claim that the mean cost has changed.

Answer 1

a)

Confidence interval estimate for population mean when population standard deviation is not known.

Given,

Number of client audit fees in the sample : Sample size : n =35

Sample mean audit cost : = 670

Sample standard deviation : s = 85

for 90% confidence level = (100-90)/100 =0.10

/2 = 0.10/2=0.05

Degrees of freedom = n-1 =35-1=34

90​% confidence interval estimate for the mean audit cost

90​% confidence interval estimate for the mean audit cost : (646,694)

b)

As Historical mean : 650 ; i.e 646 < 650 < 694 ; i.e The interval contains the historical mean ​$650

Based on your confidence​ interval, what do you think of the claim that the mean cost has​ changed?

A. The interval contains the historical mean ​$650​, which does not support the claim that the mean cost has changed.