The average health care costs per year for a sample of U.S. cities (50,000~200,0

Question

The average health care costs per year for a sample of U.S. cities (50,000~200,000 population) are $586. U.S. Department of Health and Human Services has funded several HMOs. Ten [n= 10] samples show the Sample Mean: $521.30, s = $55.80, s.e.=17.65.
a. Calculate the t score based on these data. [6 points]
b. The research hypothesis H1 is that HMOs are an improvement. Are they? [6 points] The t-score associated with alpha = 0.005 from Table 3 in the appendix is 2.576. Answer this question after comparing the calculated t score [your answer from part a] with the critical t score of 2.576.

Explanation / Answer

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a) tscore = (586 - 521.30)/(17.65) = 3.6657

b) NO, Since 586 > 521.30 + 17.65*2.576 = 566.7664(Critical Value)

Also, t score of a is greater than t-score of 2.576, so hyposthesis has to be rejected

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