Question

A data set includes 109 body temperatures of healthy adult humans for which x overbarxequals=98.2°F and s equals 0.62 degrees Upper Fs=0.62°F. Complete parts​ (a) and​ (b) below.What is the best point estimate of the mean body temperature of all healthy humans?Using the sample​ statistics, construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contain 98.6degrees°​F?

a. What does the sample suggest about the use of 98.6degrees°F as the mean body​ temperature?
b. What is the confidence interval estimate of the population mean μ​?

Answer 1

Explanation:

Given that a data set includes 109 body temperatures of healthy adult humans for which sample mean =98.2°F and s equals 0.62 degrees

Std error of mean =
`(s)/(√(n) ) \\=0.0594\\`

df = 108

Critical value for 99% t =2.581

Margin of error = 2.581*std error = 0.1533

99% confidence interval = Mean ±0.1533

=
`(98.0467, 98.3533)`

a) Since the confidence interval does not contain 98.6 degrees we reject the null hypothesis that mean = 98.6 degrees

b) confidence interval for population mean = 98.6±0.1533

=
`(98.4467, 98.7533)`