Question

An epidemiologist wishes to check that normal body temperature are indeed 98.6 degrees. They draw a random sample of 18 individuals and the sample mean is found to be 98.217 degrees with a standard deviation was .684. What can the epidemiologist conclude about body temperatures?

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 98.6 versus Ha: µ ≠ 98.6

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 98.6

Xbar = 98.217

S = 0.684

n = 18

df = n – 1 = 17

α = 0.05

Critical value = - 2.1098 and 2.1098

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (98.217 - 98.6)/[0.684/sqrt(18)]

t = -2.3756

P-value = 0.0295

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that normal body temperature is indeed 98.6 degrees.