Question

A data set includes 106 body temperatures of healthy adult humans having a mean of

98.9degrees°F and a standard deviation of 0.63degrees°F.

Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of

98.6 degrees°F as the mean body​ temperature?

What is the confidence interval estimate of the population mean μ​?

Answer 1

Let the sample size be n= 106. Let the sample mean be 7 = 98.9 and standard deviation be s =0.63. The degrees of freedom is df = (n-1)= 105 The critical t-value is obtained from the t-table. a=0.01 = 2.623 The 99% confidence interval is given as follows: =(95.9(2.023x9.03 ).98.9+(2.23% 9h03) = (98.739,99.061) The confidence limits does not contain 98.6 degrees F as the mean body temperature, this suggests that the mean body temperature is higher than 98.6 degrees F.