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 3.15 hours. A new sample of 15 audit times shows the following times in hours.

Complete parts a and b below.

3.4 4.1 4.7 3.1 4.7 2.7 3.7 3.9 4.1 3.9 2.9 3.2 4.4 3.8 4.6

A. Assume the conditions necessary for inference are met. Find a 90​% confidence interval for the mean audit time. The 90​% confidence interval to estimate the mean audit time is from _____ to _______.

B. Based on your answer to part A do you think the audit times have in fact increased?

a. Since the population mean, 3.21, is contained within the 90% confidence interval, it can be said with 90% confidence the mean audit time has NOT increased.

b. Since the population mean, 3.21, is above the 90% confidence interval, it can be said with 90% confidence the mean audit time HAS increased.

c. Since the population mean, 3.21, is below the 90% confidence interval, it can be said with 90% confidence the mean audit time HAS increased.

d. Since the population mean, 3.21, is contained within the 90% confidence interval, it can be said with 90% confidence the mean audit time HAS increased.

Answer 1

Soluton-A:

Rcode to get 90% confidence interval for mean is

auditimes <- c(3.4, 4.1, 4.7, 3.1, 4.7, 2.7, 3.7, 3.9, 4.1, 3.9, 2.9 ,3.2, 4.4, 3.8 ,4.6)
length(auditimes)
t.test(auditimes,conf.level = 0.90)

Ouptut:

data: auditimes
t = 22.833, df = 14, p-value = 1.773e-12
alternative hypothesis: true mean is not equal to 0
90 percent confidence interval:
3.519178 4.107488
sample estimates:
mean of x
3.813333
ANSWER:

90 percent confidence interval:
3.519178 and 4.107488

he 90​% confidence interval to estimate the mean audit time is from 3.52 to 4.11

rounded to 2 decimals)

Solution-b:

c. Since the population mean, 3.21, is below the 90% confidence interval, it can be said with 90% confidence the mean audit time HAS increased.