Question

A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1degreesF and a standard deviation of 0.56degreesF. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6degreesF as the mean body​ temperature?

Answer 1

Sol:

n=103

df=n-1=103-1=102

xbar=sample mean=98.1

s=samples stddev=0.56

alpha=1-0.99=0.01

alpha/2=0.01/2=0.005

t critical value in excel

==T.INV(0.005,102)

=2.62489

99% confdence interval for mean temperature is

xbar-Tc*s/sqrt(n),xbar+Tc*s/qrt(n)

98.1-2.62489*0.56/sqrt(103),98.1+2.62489*0.56/sqrt(103)

97.95516,98.24484

99% lower limit mean=97.95516

99% upper limit-98.24484

Ho:mu=98.6

Ha:mu not =98.6

it does not include 98.6

so reject null hypothesis Accept alternative hypothesis

The sample do not suggest about the use of 98.6degreesF as the mean body​temperature