Human Body Temperature: What's Normal?
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°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.
Sample Size:n = 130
Population: Adult human temperatures (Fahrenheit)
Distribution: Approximately normal
Test Statistics:x = 98.25, s = 0.73
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.
• Sketch the sampling distribution.
• Determine the critical values and add them to your sketch.
• Determine the rejection regions and shade them in your sketch.
• Find the standardized test statistic. Add it to your sketch.
• Make a decision to reject or fail to reject the null hypothesis.
• Interpret the decision in the context of the original claim.
2. If you lower the level of significance to a = 0.01, does your decision change? Explain your reasoning.
3. Test the hypothesis that the mean temperature of men is 98.6°F. What can you conclude at a level of significance of a = 0.01?
4. Test the hypothesis that the mean temperature of women is 98.6°F. What can you conclude at a level of significance of a = 0.01?
5. Use the sample of 130 temperatures to form a 99% confidence interval for the mean body temperature of adult humans.
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?
1. Test the level of significance of the correlation coefficient r. Use a = 0.05.
2. Use the regression line to predict the personal outlays when the personal income is 5.3 trillion dollars.
3. The equation used to predict sunflower yield (in pounds) is
where x1 is the number of acres planted (in thousands) and x2 is the number of acres harvested (in thousands). Use the regression equation to predict the y-values for the given values of the independent variables listed below. Then determine which variable has a greater influence on the value of y.
x1 = 2103, x2 = 2037
x1 = 3387, x2 = 3009
x1 = 2185, x2 = 1980
x1 = 3485, x2 = 3404
Organize the following data in a scatter plot. Then find the sample correlation coefficient r. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables. What can you conclude?
This solution provides assistance with the hypothesis testing problems regarding human body temperature.