What is normal, when it comes to people's body temperatures?

Question

A random sample of 550 human body temperatures had a mean of 98.35° and a standard deviation of 0.72°. (a) Construct a 99% confidence interval for the average body temperature of healthy people.

Answer 1

The sample size n=550

The mean body temperature, x bar=98.35 degrees

The standard deviation, s = 0.72 degrees.

Since the population standard deviation is not known, instead we are given the sample standard deviation, s, we will use t statistic.

The confidence interval is 99%.

alpha= (1-0.99) = 0.01. So alpha over 2 = 0.005

degrees of freedom=(n-1)=(550-1)=549

T value for 0.005, 549 from the table or calculator is = 2.58 (rounded to two decimal places)

The confidence interval formula = x̄ ± t_α/2(df) *S√n.

Plug in the values in the above formula, we get the confidence interval as = 98.35 ± 0.0792

The lower value of the confidence interval is = 98.27

The upper value of the confidence interval is = 98.43.