Posted by **Gweedo8** on Friday, March 19, 2010 at 11:01pm.

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.

- INTRO TO STATISTICS HYPOTHESIS TESTING -
**MathGuru**, Saturday, March 20, 2010 at 9:05am
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).

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