Question

A data set includes

109109

body temperatures of healthy adult humans having a mean of

98.298.2degrees°F

and a standard deviation of

0.620.62degrees°F.

Construct a

9999​%

confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of

98.6degrees°F

as the mean body​ temperature?

What is the confidence interval estimate of the population mean

muμ​?

Answer 1

Solution:

Given:

sample mean = = 98.2 and the sample standard deviation is s = 0.62.

The size of the sample is n = 109

confidence level =  99% = 0.99

So, level of significance = = 0.01

The number of degrees of freedom are df = n-1 = 109 - 1 = 108

The critical t-value for α=0.01 and df = 108,

tc = 2.622 ...Using excel function, =TINV(0.01,108)

The 99% confidence for the population mean μ:

Formula:

Calculation:

Hence, 99% confidence interval for population mean is (98.044 , 98.356)

The given population mean is = 98.6. This population mean is beyond above interval. It does not contained in the interval. Hence, we cannot suggest about the use of 98.6°F as the mean body​ temperature.

Done