Chapter 7.3, Problem 1CS

Human Body Temperature: What’s Normal?

In an article in the Journal of Statistics Education (vol. 4. no. 2), Allen Shoemaker describes a study that was reported in the Journal of the American Medical Association (JAMA).* It is generally accepted that the mean body temperature of an adult human is 98.6°F. 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°F.

$\begin{array}{l}{H}_0:\mu =98.6°\text{F}\text{(Claim)}\\ H_a:\mu \ne 98.6°\text{F}\end{array}$

Sample Size: n = 130

Population: Adult human temperatures (Fahrenheit)

Distribution: Approximately normal

Test Statistics: $\bar{x}=98.25$, s = 0.73

* Data for the JAMA article were collected from healthy men and women, ages 18 to 40, at the University of Maryland Center for Vaccine Development, Baltimore.

EXERCISES

1. Complete the hypothesis test for all adults (men and women) by performing the following steps. Use a level of significance of α = 0.05.

1. (a) Sketch the sampling distribution.
2. (b) Determine the critical values and add them to your sketch.
3. (c) Determine the rejection regions and shade them in your sketch.
4. (d) Find the standardized test statistic. Plot and label it in your sketch.
5. (e) Make a decision to reject or fail to reject the null hypothesis.
6. (f) Interpret the decision in the context of the original claim.