Question

It is generally accepted that the mean body temperature is 98.6 degrees. If a sample of size 100 resulted in a sample mean of 98.3 degrees with a standard deviation of 0.64 degrees. Does this sample suggest that the mean body temperature is actually lower than 98.6 degrees?

Answer 1

Solution:

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

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: the mean body temperature is 98.6 degrees.

Alternative hypothesis: H_a: the mean body temperature is actually lower than 98.6 degrees.

H₀: µ = 98.6 versus H_a: µ < 98.6

This is a lower 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 = 98.3

S = 0.64

n = 100

df = n – 1 = 99

α = 0.05

Critical value = -1.6604

(by using t-table or excel)

t = (98.3 – 98.6)/[0.64/sqrt(100)]

t = -4.6875

P-value = 0.0000

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean body temperature is actually lower than 98.6 degrees.