Question

A random sample of 130 human body temperatures, provided in the Journal of Statistical Education, has a mean of 98.25◦ F and a standard deviation of 0.73◦ F. A researcher named Violet believes that the commonly reported mean body temperature of 98.6◦ F is incorrect. In this problem, you will conduct a hypothesis t-test to test Violet’s claim and determine if the given data indicates that the average human body temperature is different from 98.6◦ F.

(a) Verify that the conditions are satisfied to conduct a one-sample t-test for the population mean body temperature.

(b) Formulate null and alternative hypotheses to test if the average human body temperature is different from 98.6◦ F.

(c) Conduct a hypothesis t-test at the α = 0.01 level to determine if Violet’s claim is correct and the given sample data indicates that the average human body temperature is different from 98.6◦ F. Is the result of your test significant? Explain your answer.

Answer 1

a)

• In theory, the data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ).
• The data must be reasonably random.
• The sample must be less than 10% of the population.

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 98.6
Alternative Hypothesis, Ha: μ ≠ 98.6

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (98.25 - 98.6)/(0.73/sqrt(130))
t = -5.467

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.