Question

To estimate μ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 81 full professors. The sample mean is = $77,220 and the sample standard deviation is s = $4500. A 98% confidence interval for μ is _____.

Answer 1

Answer with explanation:

Sample mean of 81 full Professor = $ 77,220

Sample Standard Deviation (S)= $ 4500

Sample mean= $77,220

$Z_{98 \text{Percent}=\frac{98}{100}}\\\\Z_{98 \text{Percent}=0.8365}\\\\Z_{\text Score=\frac{\bar x -\mu}{\sigma}}\\\\0.84=\frac{77220- \mu}{4500}\\\\\mu=77220-3780\\\\ \mu=73440$

So, When , z=98% , then Mean Salary ( μ)=73,440