Hypothesis Testing with known In a1996 article in the Journal of Statistics Educ
ID: 3151814 • Letter: H
Question
Hypothesis Testing with known
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. You are given the data below.
*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.
Temperature (in °F)
# of Adults
96.0-96.4
2
96.5-96.9
4
97.0-97.4
13
97.5-97.9
21
98.0-98.4
38
98.5-98.9
33
99.0-99.4
15
99.5-99.9
2
100.0-100.4
1
100.5-100.9
1
B. Use the frequency distribution to estimate the sample mean and standard deviation of Shoemaker’s data. (Write the entire numbers on your paper.)
(HINT: Enter the midpoint of the classes into L1 and the # of Adults into L2.)
Would you be justified in doing a z-test or a t-test to test a hypothesis about the population mean body temperature of healthy adults using this data? Explain.
Temperature (in °F)
# of Adults
96.0-96.4
2
96.5-96.9
4
97.0-97.4
13
97.5-97.9
21
98.0-98.4
38
98.5-98.9
33
99.0-99.4
15
99.5-99.9
2
100.0-100.4
1
100.5-100.9
1
Explanation / Answer
We can use t test, but compared to population size of whole human beings in the world, sample size is not proportionate to population size.
It would be ideal if sample size is increased.
Temp Mid pt No of adults X*f x^2*f 96.0-96.4 95.95-96.45 96.2 2 192.4 18508.88 96.5-96.9 96.45-96.95 96.7 4 386.8 37403.56 97.0-97.4 96.95-97.45 97.2 13 1263.6 122821.9 97.5-97.9 97.45-97.95 97.7 21 2051.7 200451.1 98.0-98.4 97.95-98.45 98.2 38 3731.6 366443.1 98.5-98.9 98.45-98.95 98.7 33 3257.1 321475.8 99.0-99.4 98.95-99.45 99.2 15 1488 147609.6 99.5-99.9 99.45-99.95 99.7 2 199.4 19880.18 100.0-100.4 99.95-100.45 100.2 1 100.2 10040.04 100.5-100.9 100.45-100.95 100.7 1 100.7 10140.49 130 12771.5 1254775 Mean 12771.5/130 98.24231 E(x^2) 1254775/130 9652.113 Variance 0.561672 Std dev 0.749448Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.