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.
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: Ha: the mean body temperature for all healthy adults is not equal to the traditional 98.6 degrees.
H0: µ = 98.6 versus Ha: 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.
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