Question

it has long been stated that the mean temperature of humans is 98.6°f. however, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°f. they measured the temperatures of 56 healthy adults 1 to 4 times daily for 3 days, obtaining 250 measurements. the sample data resulted in a sample mean of 98.3°f and a sample standard deviation of 1°f. use the p - value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°f at the α = 0.01 level of significance.

ho: μ = 98.6°f
h₁: μ < 98.6°f

find the test statistic.

lo = - 4.74
(round to two decimal places as needed)

the p - value is 0.000
(round to three decimal places as needed)

what can be concluded?

a. do not reject ho since the p - value is not less than the significance level
b. reject ho since the p - value is not less than the significance level
c. do not reject ho since the p - value is less than the significance level
d. reject ho since the p - value is less than the significance level

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing using the P - value approach, if the P - value < \(\alpha\) (significance level), we reject the null hypothesis \(H_0\). If the P - value \(\geq\alpha\), we do not reject the null hypothesis \(H_0\).

Step2: Compare the P - value and \(\alpha\)

We are given that \(\alpha = 0.01\) and the P - value \(= 0.000\). Since \(0.000<0.01\) (i.e., P - value < \(\alpha\)).

Answer:

D. Reject \(H_0\) since the P - value is less than the significance level.