Question

A current survey of 38 lawyers found an average salary of $120,000, with a sample standard deviation of $10,000. We don’t know the true population mean or variance for lawyers’ salaries.

Suppose that US news publishes an article saying the average lawyer’s salary in the US is $125,000, and you want to test for whether the true average salary is different than that amount

1. What is the null and alternative hypothesis for the above test? (1 POINT)

2. What are the critical values for the above hypothesis test, at the 90, 95, and 99% confidence levels? (1 POINT)

Critical Values:

3. What is the test statistic for the above hypothesis test? Not required for the point of extra credit, but also can you determine the RANGE of the p-value? (1 POINT)

4. At what significance levels (alpha levels) could you reject the null hypothesis, and why? (1 POINT)

5. If instead of 38 lawyers you had found the mean and standard deviation you found above but from a sample of 85 lawyers, what would happen to the size of the test statistic and p-value? Would you be more or less likely to reject the null hypothesis than before?    

(2 POINT)

Answer 1