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 $680. To determine if this cost has​ changed, the firm randomly samples 35 client audit fees. The sample mean audit cost was $710 with a standard deviation of 75

1) Develop a 90% confidence interval estimate for the mean audit cost. ($__,$__)

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

- The interval does not contain the historical data mean $710, which supports claim the mean cost has changed.

- The interval contains historical data mean $710, which supports the claim the mean cost has changed.

- The interval does not contains historical data mean $710, which does not support the claim it has changed.

- The interval contains historical data mean $690, which does not support the claim the mean cost has changed.

Answer 1

1)

sample mean, xbar = 710
sample standard deviation, s = 75
sample size, n = 35
degrees of freedom, df = n - 1 = 34

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.691

ME = tc * s/sqrt(n)
ME = 1.691 * 75/sqrt(35)
ME = 21.4373

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (710 - 1.691 * 75/sqrt(35) , 710 + 1.691 * 75/sqrt(35))
CI = (688.56 , 731.44)

2)

- The interval contains historical data mean $690, which does not support the claim the mean cost has changed.