Question

A data set includes 107 body temperatures of healthy adult humans having a mean of 98.7degreesF and a standard deviation of 0.72degreesF. 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.) What does this suggest about the use of 98.6degreesF as the mean body​ temperature? A. This suggests that the mean body temperature could be higher than 98.6degreesF. B. This suggests that the mean body temperature could very possibly be 98.6degreesF. C. This suggests that the mean body temperature could be lower than 98.6degreesF.

Answer 1

Solution:

Given: a data set includes 107 body temperatures of healthy adult humans having a mean of 98.7^o F and a standard deviation of 0.72^o F

That is:

Sample size = n = 107

Sample mean =

Sample standard deviation = s = 0.72

Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans.

where

where t_c is t critical value for c = 99% confidence level

df = n - 1 = 107 - 1 = 106

Look in t table for df = 106 and two tail area = 1 - 0.99 = 0.01 and find t critical value.

Since df = 106 is not in table, we look for its previous df = 100 and find t critical value.

t critical value = t_c = 2.626

Thus

Thus

Thus the confidence interval estimate of the population mean is :

What does this suggest about the use of 98.6degreesF as the mean body​ temperature?

Since confidence interval includes 98.6^o F , correct option is:

B. This suggests that the mean body temperature could very possibly be 98.6degreesF.