Question

A data set includes 106 body temperatures of healthy adult humans having a mean of 98.7degreesF and a standard deviation of 0.66degreesF. 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? Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... What is the confidence interval estimate of the population mean mu​? nothingdegreesFless thanmuless than nothingdegreesF ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

degrees of freedom = n - 1 = 106 - 1 = 105

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

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

= 2.623 * (0.66 / 106)

Margin of error = E = 0.168

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

- E < < + E

98.7 - 0.168 < < 98.7 + 0.168

( 98.532 < < 98.868 )

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