Question

A data set includes 106 body temperatures of healthy adult humans having a mean of 98.9 degrees and a standard deviation of 0.63 degrees. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6 degrees as the mean body​ temperature?

What is the confidence interval estimate of the population mean μ​?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 98.9

sample standard deviation = s = 0.63

sample size = n = 106

Degrees of freedom = df = n - 1 = 106 - 1 = 105

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,105 = 2.623

Margin of error = E = t/2,df * (s /n)

= 2.623 * ( 0.63 / 106)

Margin of error = E = 0.16

The 99% confidence interval estimate of the population mean is,

- E < < + E

98.9 - 0.16 < < 98.9 + 0.16

( 98.74 < < 99.06 )

This suggests that the mean body temperature could be higher than 98.6 degrees F.