Question

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) 51400-49600/(950/√36)=11.368=z
(c) P=6.17 x10-30
(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.

Answer 1

I would consider this a one-tailed 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 two-tailed (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 one-tailed in that direction). Therefore, Ho would be rejected in favor of Ha as you concluded in e).