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

The 99% confidence interval estimate for the mean is 97.9576 ≤ μ ≤ 98.246

A) This suggests that the mean body temperature could very possibly be 98.6 °F

Explanation:

The number of body temperatures, n = 103

The mean body temperature,
`\bar x` = 98.1

The standard deviation, s = 0.56

Confidence interval required = 99%

Confidence interval, CI is given by

`CI=\bar{x}\pm z(s)/(√(n))`

Plugging in the values we get;

z = 2.56 at 99%

`CI=98.1}\pm 2.56* (0.56)/(√(103))`

Therefore, we have

`\mu_(min) = 97.9579 , \ \mu_(max) = 98.242`,

The statistical result suggest that at 99% confidence level, the sample mean temperature is likely to be 98.1 °F