A random sample of 130 human body temperatures had a mean of 98.25 degrees and a standard deviation of 0.73 degrees.

Question

A random sample of 130 human body temperatures had a mean of 98.25 degrees and a standard deviation of 0.73 degrees. Does the data indicate that the average body temperature for healthy humans is different from 98.6 degrees? (a) Use the p-value approach with α = 0.1. (b) Use the critical value approach with α = 0.1. (c) Compare the conclusions from parts a and b. are they the same?

Answer 1

Ho: mu = 98.6

Ha: mu != 98.6

Since the sample size is very large, we can use the z-statistic.

z = (sample mean - population mean)/(sample standard deviation/square root(sample size) =

(98.25 - 98.6)/(0.73/sqrt(130)) = -5.47

p-value = P(z > 5.47) + P(z < -5.47) = 2 * P(z < -5.47) = 0, which is less than alpha = 0.1, can can reject Ho.

For alpha = 0.1, critical values > z score for 0.95 and < z score for 0.05: -1.645 and 1.645.

z = -5.47 < -1.645, so can reject Ho this way as well