MAT152 Statistical Methods I

MAT 152 Lab (Part 3) Name: Due Date: Mar 23

The establishment of normal body temperature comes from the research of Carl Wunderlich. In 1861 he

released data on the temperatures of 25,000 people. It was Carl Wunderlich who established 98.6 as the norm. Up until 1990, very little was done to refute his established norms. It was until the publication of “A

Critical Appraisal of 98.6” appeared that the medical community began to make a fuss. Now many medical

papers, theories, accusations and studies have proven that 98.6 is not normal.

In this lab we will investigate this issue:

In a1996 article in the Journal of Statistics Education (vol. 4, no. 2), entitled “A Critical Appraisal of 98.6”, Allen Shoemaker describes a study that was reported in the Journal of the American Medical Association

(JAMA). * It is generally accepted that the mean body temperature of an adult human is 98.6 F. In his article, Shoemaker uses the data from the JAMA article to test this hypothesis. *Data for the JAMA article were collected from healthy men and women, ages 18 to 40, at the University of Maryland Center for Vaccine Development, Baltimore.

** Round any probabilities (areas) to four decimal places, any standardized scores to two decimal places, and round the standard error to four decimal places.**

Make sure you use the correct calculator in StatCrunch.

Questions:

1. From Part 1 Lab (questions #2 & #3), restate the sample mean, the sample standard deviation, and the sample size. Include the correct symbols and units. (6 points)

2. Reviewing your answer for #1, should you use the normal distribution curve or the t distribution curve for

probability questions? Explain in a complete sentence. (6 points)

3. Sketch the sampling distribution curve showing the generally accepted mean and all labels required on the axis. What is the total area under this curve? Using the sample standard deviation and sample size, what is the standard error of the mean? (16 points)

4. Suppose a mean temperature was found to be 98.7 F for another sample of 130 adults. (30 points)

a. What is the standardized score for the mean temperature of 98.7 F ? Show the calculation.

b. Sketch the standardized score on the curve (label all parts of the curve).

c. How does this mean temperature compare to the generally accepted mean? Explain in a complete sentence.

d. What is the probability that a mean temperature is above 98.7 F ? Use the correct shorthand notation.

e. Show the probability on the curve (label and shade all details on part b).

5. Suppose a mean temperature was found to be 98.246 F for another sample of 130 adults. (36 points)

a. What is the standardized score for the mean temperature of 98.246 F ? Show the calculation.

b. Sketch the standardized score on the curve (label all parts of the curve).

c. How does this mean temperature compare to the generally accepted mean? Explain in a complete sentence.

d. What is the probability that a mean temperature is below 98.246 F ? Use the correct shorthand notation.

e. Show the probability on the curve (label and shade all details on part b).

f. If 98.6 F is really the true mean, is it unusual to find a mean temperature below 98.246 F ?

Does this result make you question the generally accepted mean of 98.6 F ? Explain in a complete sentence.

6. What is the probability that a mean temperature is between 98.246 F and 98.7 F ? Show the standardized scores and the probability on the curve (label and shade all details and parts of the curve). Use the correct shorthand notation. You will need to sketch the curve but you can use the information you already calculated in previous questions to help you with the standardized scores. (6 points)