Question

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.1 degrees Fahrenheit and a standard deviation of 0.56 degrees Fahrenheit. 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 Fahrenheit as the mean body temperature? What is the confidence interval estimate of the population mean? (MUST !Round to 3 decimal places)

Answer 1

a.)

n = 108

since n > 30, we can assume that distribution is normal and can use Z-score to solve.

sample mean, = 98.1

sample standard deviation, s = 0.56

For 99% Confidence interval, z = 2.57

Standard Error, SE = s /

SE = 0.56 /

SE = 0.56 / 10.3923

SE = 0.0538

Margin of Error = z * SE = 0.1382

Now, Confidence Interval = Margin of Error = 98.1 0.1382

Confidence Interval = (97.9618, 98.2382)

b.)

Since 98.6 is more than upper limit of confidence interval.

This suggests that Mean Body Temperature can be lower than 98.6

c.)

confidence interval estimate of the population mean is (97.9618, 98.2382)