It has long been stated that the mean temperature of humans is 98.6 degree F. Ho

Question

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 temerature of humans is less that 98.6 degrees F. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days. obtaining 600 measurements. The sample data resulted in a sample mean of 97.9 degrees F and a sample standard deviation of 0.8 degrees F.

(A) Using the classical approach, judge whether the mean temperature of humans is less than 98.6 at the a=0.01 level of significance.

(B) The P-value is approximately ___ (Round to 4 decimal places as needed.)

Explanation / Answer

Here the hypothesis for the testing is,

H0 : µ = 98.6 Vs H1 : µ < 98.6

Since the test is left sided.

And we have given the information regarding sample and population standard deviation is unknown.

So we use t-test here.

The test statistic is,

t = (Xbar - µ) / [ s/sqrt(n) ]

where Xbar is mean of sample = 97.9

s is standard deviation of sample = 0.8

n is the number of observations = 148

t = ( 97.9 -98.6) / [ 0.8 /sqrt(148) ]

= -0.7 / 0.0658 = -10.64

We find critical value by using EXCEL :

=tinv(2*alpha , deg_freedom)

where alpha = 0.01

deg_freedom = n - 1

This will gives us critical value 2.35198

Here test statistic < critical value

Reject H0 at 1% level of significance.

Conclusion : The mean temperature of humans is less than 98.6

P-value in EXCEL syntax is,

=tdist(x,deg_freedom,tails)

x is the test statistic value

deg_freedom = n - 1

tails = 1

P-value = 2.83432E-20

P-value = 0.0000

P-value is very small.

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