An alumni association at a university wants to gather data on the annual earning

Question

An alumni association at a university wants to gather data on the annual earnings of former students employed as accountants who earned their CPA licenses one year ago. After taking a random sample from university records of all accounting students who graduated a year ago, the alumni association sent out a survey to the selected individuals in the sample and received 75 responses.

An analyst for the alumni association used the responses to calculate a 95% confidence interval for the mean salary of accountants one year after obtaining their CPA licenses, finding the interval to be $64,000 to $89,000 per year. Which of the following statements is the correct interpretation of this interval in context? Read carefully!

a) The alumni association can be confident, based on the method used to calculate the interval, that 95% of the accountants in the university's sample of 75 earned between $64,000 and $89,000 per year.

b) There is a 95% chance, based on the method used to calculate the interval, that this particular interval, $64,000 to $89,000 per year, contains the true mean salary of the university's accounting graduates one year after obtaining their CPA licenses.

c) The alumni association can be confident, based on the method used to calculate the interval, that the mean salary of all university students in the U.S. who graduated one year ago is $64,000 and $89,000 per year.

d) The alumni association can be 95% confident, based on the method used to calculate the interval, that a large majority of the university's accounting graduates one year after obtaining their CPA license earn between $64,000 to $89,000 per year, based on the method used to construct the interval.

e) The alumni association can be 95% confident, based on the method used to calculate the interval, that any one of the university's accounting graduates one year after obtaining a CPA license will earn between $64,000 and $89,000 per year.

f) The alumni association can be 95% confident, based on the method used to calculate the interval, that the true mean salary of the university's accounting graduates one year after obtaining their CPA licenses is between $64,000 and $89,000 per year.

Explanation / Answer

Correct interpretation is
" The alumni association can be 95% confident, based on the method used to calculate the interval, that the true mean salary of the university's accounting graduates one year after obtaining their CPA licenses is between $64,000 and $89,000 per year."

Option F is correct.

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