Question

1. The data for this problem set are derived from an article in the Journal of the

   American Medical Association entitled “A Critical Appraisal of 98.6 Degrees F, the

   Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich” (Mackowiak, Wasserman, and Levine 1992).
2. Suppose that someone claims that the true population standard deviation of body temperatures is greater than 0.6 degrees. What are the null and alternative hypotheses? What is the value of this test statistic? Can you reject the null hypothesis at the 1‐percent level of significance? Show your work and explain.

3. Results in r:  t = -5.4548, df = 129, p-value = 2.411e-07

4. Standard deviation 0.7331832

   99 percent confidence interval:
   98.08111 - 98.41735

   sample estimates: mean of x =98.24923

Answer 1

Null: s.d of body temperature <= 0.6
Alternate: s.d of body temperature > 0.6

T =
N-1)(s/00)

Reject the null hypothesis at the significance level , if
2 (a,N-I)
  

T = 129*(0.7331832/0.6)^2 = 192.625
T > critical value
Therefore, null is rejected at 1% level of significance