Question

A survey of CPAs across the United States found the average net income for sole proprietor CPAs is $114,300. Because this survey is now more than 5 years old, an accounting researcher wants to test this figure by taking a random sample of 36 sole proprietor accountants in the United States to determine whether the average net income has increased. Only 500 sole proprietorships practice in the US. The sample of 36 sole proprietor accountants had a mean of $119,000 with a standard deviation of $12,000.

Construct a 99% confidence interval for the population mean net income for sole proprietor CPAs.

Show your work! Formula(s), substitutions, answers! Please round your z or t value to 3 decimal places, and your final answers to whole numbers.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $ 119,000

sample standard deviation = s = $ 12,000

sample size = n = 36

Degrees of freedom = df = n - 1 = 36 - 1 = 35

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,35 = 2.724

Margin of error = E = t/2,df * (s /n)

= 2.724 * ( 12000 / 36)

Margin of error = E = $ 5448

The 99% confidence interval estimate of the population mean is,

  ± E  

= $ 119,000 ± $ 5448

= ( $ 113,552 to $ 124,448 )