Question

Using the sample​ statistics, construct a 9999​% confidence interval estimate of the mean body temperature of all healthy humans. do the confidence interval limits contain 98.6degrees°​f? what does the sample suggest about the use of 98.6degrees°f as the mean body​ temperature?

Answer 1

Given that a data set includes 105 body temperatures of healthy adult humans for which $\bar{x}=98.7^oF$ and $s=0.64^oF$.


Part A:

What is the best point estimate of the mean body temperature of all healthy humans?

The sample mean is the point estimate of the population mean.

Given that the sample mean is 98.7 degrees F, therefore, the best point estimate is 98.7 degrees F.



Part B:

Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.

Since the sample size is large, we can assume that the population is approximately normal.

The 99% confidence interval of a data set with sample mean $\bar{x}=98.7$ and sample standard deviation, s = 0.64 and degree of freedom = 105 - 1 = 104 is given by:

$C.I.=\bar{x}\pm1.665\left( \frac{s}{\sqrt{n}} \right) \\ \\ =98.7\pm1.665\left( \frac{0.64}{\sqrt{105}} \right) \\ \\ =98.7\pm1.665(0.0625) \\ \\ =98.7\pm0.104=\bold{(98.596, \ 98.804)}$

It can be seen from above that the confidence interval is between 98.596 and 98.804 which contains 98.6 degrees F.

This suggests that the mean body temperature could very possibly be 98.6 degrees F.