It has long been stated that the mean temperature of humans is 98.6degreesF. How

Question

It has long been stated that the mean temperature of humans is 98.6degreesF. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6degreesF. They measured the temperatures of 148 healthy adults 1 to 4 times daily for 3 days, obtaining 700 measurements. The sample data resulted in a sample mean of 98.2degreesF and a sample standard deviation of 0.7degreesF. (a) Using the classical approach, judge whether the mean temperature of humans is less than 98.6degreesF at the alphaequals0.01 level of significance. (b) Approximate the P-value.

Explanation / Answer

Solution:

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 = 98.2

s is standard deviation of sample = 0.7

n is the number of observations = 148

t = ( 98.2 -98.6) / [ 0.7 /sqrt(148) ]

= -0.4 / 0.0575= -6.96

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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