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 2.86 hours. A new sample of 15 audit times shows the following times in hours. Complete parts a and b below.

3.8
3.4
4.5
3.2
4.6
2.9
2.5
2.7
4.7
3.3
4.5
4.4
3.1
3.7
4.7

Assume the conditions necessary for inference are met. Find a 99% confidence interval for the mean audit time.

Answer 1

The given data is

X <- c(3.8,3.4, 4.5,3.2,4.6,2.9,2.5,2.7,4.7,3.3,4.5,4.4,3.1,3.7,4.7)
length(X)
mean(X)
sd(X)

The sample mean is , sample standard deviation is and sample size is .

Since the population standard deviation is not known, we use t-distribution.

The confidence interval for true mean based on the sample data is

So the 99% CI for mean is