It has long been stated that the mean temperature of humans

It has long been stated that the mean temperature of humans in 98.6 degrees F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F. They measured the temperature of 148 healthly adults 1 to 4 times daily for 3 days, obtaining 500 measurements. The sample data resulted in a sample mean of 98.1 degrees F and sample standard deviation of 0.7 degrees F.

(a)Using the classical approach, judge whether the mean temperature of humans is less than 98.5 degrees F at the a=0.001 level of significance.

(b)Approximate the P-Value

(a)Choose the correct answer below.

a) Do no reject H0 since the test statisitc is not less than the critical value.

b) Reject H0 since the test statistic is not less than the critical value.

c) Do not reject H0 since the test statistic is less than the critical value.

d) Reject H0 since the test statisitc is less than the critical value.

(b) The P-value is approximately_

Solution

Using the classical approach, judge whether the mean temperature of humans is less than 98.5 degrees F at the a=0.001 level of significance.

Null hypothesis H₀ : population mean = 98.5

Alternative hypothesis: H_A : population mean <   98.5

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                      mean=

98.5

Level of Significance

0.001

Standard Deviation

0.7

Sample Size

148

Sample Mean

98.1

Standard Error of the Mean

0.0575

Z Test Statistic

-6.95

Lower-Tail Test

Lower Critical Value

-3.090

p-Value

0.0000

Reject the null hypothesis

(a)Choose the correct answer below.

a) Do no reject H0 since the test statisitc is not less than the critical value.

b) Reject H0 since the test statistic is not less than the critical value.

c) Do not reject H0 since the test statistic is less than the critical value.

d) Reject H0 since the test statisitc is less than the critical value.

(b) The P-value is approximately_     0.0000