INTRO TO STATISTICS HYPOTHESIS TESTING
posted by Gweedo8 .
Math Horizons is a publication of the Mathematical Association of America. A recent issue reports that in the United States, graduating mathematics majors who also have studied actuarial
science have an average first year income of 49,600. Suppose a random sample of36 recent such graduates in the Denver/Boulder region showed that they were earning an average of
$51,400 with a sample standard deviation of $950. Does the information indicate that thepopulation mean salary is higher than the national ave?
Here is my work thus far:
(a) H0:µ=49600 (claim), Ha:µ≠49600
(b) 5140049600/(950/√36)=11.368=z
(c) P=6.17 x1030
(d) R.R. >2.326
(e) Reject b/c there is enough evidence at a 1% level of significance to support that Denver/Boulder regions is higher than the national average.

I would consider this a onetailed test (state Ha as µ > 49600). When using a "does not equal" with Ha, you are just looking for a difference and the test would be twotailed (either direction). Your test statistic calculation looks correct. This test statistic would also exceed most commonly used positive critical or cutoff values (positive because Ha is onetailed in that direction). Therefore, Ho would be rejected in favor of Ha as you concluded in e).