Question

Confidence Intervals Example: Body Temperature What is the mean body temperature of a healthy human? According to your thermometer it is probably 98.6° F. A study to estimate the mean healthy body temperature produced the following results for 93 randomly selected healthy subjects. TEMP 98 97 98 98 98 98 98 97 97 98 98.1 98 98 98 97 97 97 98 97 98 97 97.1 98 98 97 96 96 98 98 98.8 98 98.8 98.8 97.6 97 98 97 96 98 97 98 97 97 98 98 98 98.1 98 97 98 98 99.1 97 97 97 98 98 98 98 98 98 98 98 98.6 98.8 98 98 98 97 97 98.1 97 98 98 98 98 98 97 98 98 Mean - 98.12366 Standard Deviation = 0.646798 Answer the following questions a. What is the distribution of the sample mean healthy body temperature for samples of this size? b. What does the mean shown below the table above represent? Is it a parameter or a statistic? c. What is the "point estimate" of the mean body temperature of a healthy human based on this sample? d. Do we expect the mean body temperature of a healthy human to be exactly 98.12366° F? Explain. Use the data above to create a 95% confidence interval for the true mean healthy body temperature.

Answer 1

Let X denotes the body temperature of a healthy human.

µ : mean body temperature of a healthy human.

n = sample size = 93.

a) The sampling distribution of mean is approximately normal with mean = µ = 98.6

b) Sample mean is a function of sample observation. Hence it is statistic.

c) Point estimate of mean body temperature(µ) is sample mean.

d) Since sample mean is unbiased estimator of population mean.

e) Since population standard deviation is not known. Sample variance is an unbaised estimator of population variance.