Suppose the mean salary for full professors in the United States is believed to

Question

Suppose the mean salary for full professors in the United States is believed to be $61,650. A sample of 15 full professors revealed a mean salary of $64,250 with a standard deviation of $5,000. Can it be concluded that the average salary has increased using a 1% level of significance? If a test of significance is warranted clearly indicate the following steps:

Step 1: (State the null and alternative hypothesis.)

Step 2: (Calculate the test statistic) T/Z =

Step 3: (Find the p-value) =

Step 4: (State the Conclusion in sentence form) Reject/Accept the null hypothesis because

Explanation / Answer

Step 1: (State the null and alternative hypothesis.)

Let mu be the population mean

Null hypothesis: mu=61,650

Alternative hypothesis: mu>61,650

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Step 2: (Calculate the test statistic)

T = (xbar-mu)/(s/vn)

=(64250-61650)/(5000/sqrt(15))

=2.01

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Step 3: (Find the p-value) =

The degree of freedom =n-1=15-1=14

It is a right-tailed test.

So the p-value= P(t with df=14 >2.01) =0.0321 (from student t table)

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Step 4: (State the Conclusion in sentence form) Reject/Accept the null hypothesis because

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