Question

Here are the daily average body temperatures (in degrees Fahrenheit) for 20 healthy

adults:

98.74 98.83 96.80 98.12 97.89 98.09 97.87 97.42 97.30 97.84

100.27 97.90 99.64 97.88 98.54 98.33 97.87 97.48 98.92 98.33

Do these data give evidence that the mean body temperature for all healthy adults is not

equal to the traditional 98.6 degrees? State the hypotheses, find a

P -value, and write a summary of your results.

Answer 1

Solution:

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

Null hypothesis: H₀: the mean body temperature for all healthy adults is equal to the traditional 98.6 degrees.

Alternative hypothesis: H_a: the mean body temperature for all healthy adults is not equal to the traditional 98.6 degrees.

H₀: µ = 98.6 versus H_a: µ ≠ 98.6

This is a two tailed test.

We assume level of significance = α = 0.05

The test statistic formula for this test is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

Sample mean = Xbar = 98.203

Sample standard deviation = S = 0.803473381

Sample size = n = 20

Degrees of freedom = df = n – 1 = 20 – 1 = 19

Critical values = -2.0930 and 2.0930

(by using t-table)

t = (Xbar - µ)/[S/sqrt(n)]

t = (98.203 – 98.6)/[ 0.803473381/sqrt(20)]

t = -0.397/0.1797

t = -2.209237618

Test statistic = t = -2.209237618

P-value = 0.0396

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis H₀

There is sufficient evidence to conclude that the mean body temperature for all healthy adults is not equal to the traditional 98.6 degrees.