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 F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6. 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 98.1F and a sample deviation of .8F.

(a) using the classical approach, judge whather the mean temperature of humans is less than 98.6F at the a=.01 level of significance.

(b) Approx. the P-Value

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a. Choose the correct answer below

1. Reject Ho, since the test statistic is less than critical value

2. Do not reject Ho, since the test statistic is less than critical value.

3. Do not rejct Ho since the test statistif is not less than critical value

4. Reject Ho since the test statistc is not less than critical value.

(b) The P-Value is Approx. ______

Solution

(a) Let mu be the population mean

Ho: mu=98.6 (i.e. null hypothesis)

Ha: mu<98.6 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(98.1-98.6)/(0.8/sqrt(148))

=-7.6

It is a left-tailed test.

Given a=0.01, the critical value is Z(0.01)= -2.33 (from standard normal table)

Since Z=-7.6 is less than -2.33, we reject Ho.

Answer: Reject Ho, since the test statistic is less than critical value

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(b) The p-value= P(Z<-7.6)=0 (from standard normal table)