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 of. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6

Solution

(a) Let mu be the population mean

The test hypothesis:

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)/(0.7/sqrt(148))

=-8.69

It is a left-tailed test.

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

The rejection region is if Z<-2.33, we reject the null hypothesis.

Since Z=-8.69 is less than -2.33, we reject the null hypothesis.

Answer: b. Reject H0 since the test statistic is less than the critical value.

---------------------------------------------------------------------------------------------------------------

(b) The p-value= P(Z<-8.69) = 0 (from standard normal table)