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# Hypothesis Test for the Average Income of a Sold Proprietor CPA

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A ten year old survey found that the average income of sole proprietor CPA's was \$74,914. To update this information, a new survey of 112 proprietor CPA's was taken and it showed a mean of \$74,695. Use a 5% level of significance to test whether the average income sole proprietor CPA's has increased. Assume a population standard deviation of \$14.530. Report the value. What is is your conclusion?

##### Solution Summary

The solution reports the value for the average income of sold proprietor CPA.

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Solution.

Null hypothesis H0: mu<=\$74,914
Alternative hypothesis Ha: mu>\$74,914

Given xbar=74695, n=112, sigma=14530. ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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