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 3.25 hours. A new sample of 10 audit times shows the following times in hours: 4.2, 3.7, 4.8, 2.9, 3.1, 4.5, 4.2, 4.1, 5.0, 3.4 a) Assume the conditions necessary for inference are met. Find a 90% confidence interval estimate for the mean audit time. b) Based on your answer to part a, do you think that the audit times have, in fact, increased?

Answer 1

The 90% confidence interval for the mean audit time is (3.583 ; 4.397) and it can be concluded that the mean audit time has increased since last year's audit time does not fall within the confidence interval.

• Samples = 4.2, 3.7, 4.8, 2.9, 3.1, 4.5, 4.2, 4.1, 5.0, 3.4

• Sample size, n = 10

Using calculator to calculate the sample mean and standard deviation :

• Mean, μ = 3.99
• Standard deviation, σ = 0.703

The confidence interval can be calculated using the relation :

Since the sample size is small; we use a t-distribution ;

• Zcritical, Z* at 0.1 ; df =(10 - 1) = 9 = 1.833

• Standard Error(SE) = (σ/√n) = 0.703/√10 = 0.222

• C. I = μ ± Z*(SE)

Lower boundary = 3.99 - 1.833(0.222) = 3.583

Upper boundary = 3.99 + 1.833(0.222) = 4.397

Therefore, the confidence interval estimate for the mean audit time is (3.583 ; 4.397)

B.)

Since the audit time recorded last year does not fall within the calculated confidence interval then the audit time has increased.

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