Question

It has been long stated that the mean temperature of humans is 98.6 degrees Faranheit. However, two researchers currently involved in the subject though that the mean temperature of humans is less than 98.6 degrees. They measured the temperatures of 44 healthy adults 1 to 4times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.3 and a sample standard deviation of 1.1 degrees. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humansis less than 98.6 degrees at the a= 0.01 level of significance.

State the hypothesis.

Find the test statistic.

to=? round two decimals as needed

reject or fail to reject and why

Answer 1

Null Hypothesis(H0):

The mean temperature of humans is not significantly less than 98.6 degrees. 98.6⁰ F. (Hypothesised population mean, =98.6).

Alternative Hypothesis(H1):

The mean temperature of humans is significantly less than 98.6 degrees. < 98.6⁰ F. (Left-tailed test).

Test statistic, Z:

Sample size, n =200

Sample mean, =98.3

Sample standard deviation, s =1.1

The test statistic, Z =(​​​​​​)/(s/​​​​​​) =(98.3 - 98.6)/(1.1/​​​​​​) = -3.86

p-value:

For Z =-3.86 (or 3.86), for a left-tailed test (or one-tailed test), at 0.01 significance level, the p-value =0.000057

Decision criteria (p-value approach):

If the p-value < given significance level, reject H0. Otherwise do not reject H0.

Conclusion:

Since the p-value of 0.000057 < 0.01 significance level, we reject the null hypothesis(H0) at 1% significance level.

Thus, we have a sufficient statistical evidence to claim that the mean temperature of humans is significantly less than 98.6 degrees Faranheit.