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# Level of Significance (Human Body Temperature Test)

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In an article in the Journal of Statistics Education (vol. 4, no. 2, 1996), Allen Shoemaker describes a study that was reported in the Journal of the American Medical Association.* It is generally accepted that the mean body temperature of adult humans is 98.6 degF . In his article, Shoemaker uses the data from the JAMA article to test this hypothesis. Here is a summary of his test.

Claim: The body temperature of adults is 98.6 degF.

Ho; U = 98.6 F (Claim) Ha: u not equal to 98.6 F
Sample size N = 130
Distribution: Approximately normal
Test Statistics; x = 98.25, s = .73
Men's Temperatures
96 | 3
96 | 7 9
97 | 0 1 1 1 2 3 4 4 4 4
97 | 5 5 6 6 6 7 8 8 8 8 9 9
98 | 0 0 0 0 0 0 1 1 2 2 2 2 3 3 4 4 4 4
98 | 5 5 6 6 6 6 6 6 7 7 8 8 8 9
99 | 0 0 0 1 2 3 4
99 | 5
100 | 0
Key 96/3 = 96.3

Women's Temperatures

96 | 4
96 | 7 8
97 | 2 2 4
97 | 6 7 7 8 8 8 9 9 9
98 | 0 0 0 0 0 1 2 2 2 2 2 2 3 3 3 4 4 4 4 4
98 | 5 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9
99 | 0 0 1 1 2 2 3 4
99 | 9
100 | 8 Key: 96/ 4 = 96.4

1. Complete the hypothesis test for all adults (men and women) by performing the following steps. Use a level of significance of a = 0.05 .
(a) Sketch the sampling distribution.
(e) Make a decision to reject or fail to reject the null hypothesis.
(f ) Interpret the decision in the context of the original claim.

2. If you lower the level of significance to .01 does your decision change? Explain your reasoning.

3. Test the hypothesis that the mean temperature of men is 98.6 What can you conclude at a level of
significance of .01?

4. Test the hypothesis that the mean temperature of women is 98.6 What can you conclude at a
level of significance of .01?

5. Use the sample of 130 temperatures to form a 99% confidence interval for the mean body

6. The conventional "normal" body temperature was established by Carl Wunderlich over 100 years
ago. What, in Wunderlich's sampling procedure, do you think might have led him to an incorrect
conclusion?