It has long been stated that the mean temperature of humans

It has long been stated that the mean temperature of humans is 98.6 degree F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degree F. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 500 measurements. The sample data resulted in a sample mean of 98.1 degree F and a sample standard deviation of 0.7 degree F. Using the classical approach, judge whether the mean temperature of humans is less than 98.6 degree F at the alpha = 0.01 level of significance. Approximate the P-value. Click here to view the t-Distribution .Area in Right Tail. Choose the correct answer below. Reject H_0 since the test statistic is not less than the critical value. Do not reject H_0 since the test statistic is not less than the critical value. Do not reject H_0 since the test statistic is less than the critical value. Reject H_0 since the test statistic is less than the critical value. The P-value is approximately .(Round to four decimal places as needed.)

Solution

Set Up Hypothesis
Null, H0: U=98.6
Alternate, H1: U<98.6
Test Statistic
Population Mean(U)=98.6
Sample X(Mean)=98.1
Standard Deviation(S.D)=0.7
Number (n)=500
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =98.1-98.6/(0.7/Sqrt(500))
to =-15.972
| to | =15.972
Critical Value
The Value of |t | with n-1 = 499 d.f is 2.334
We got |to| =15.972 & | t | =2.334
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -15.9719 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

[ANSWERS]
a.
Reject Ho, test statistic is less than tha critical value
b.p-value is zero