FOR THIS PROBLEM PLEASE USE ALL THE DATA BOTH MEN AND WOMEN'S TEMPERATURES Mens Temperatures (in degrees Fahrenheit) 96 3 97 7 9 97 0 1 1 1 2 3 4 4 4 4 97 5 5 6 6 6 7 8 8 8 8 9 9 98 0 0 0 0 0 0 1 1 2 2 2 2 3 3 4 4 4 4 98 5 5 6 6 6 6 6 6 7 7 8 8 8 9 99 0 0 0 1 2 3 4 99 5 100 Key 96 3 96 3 Womens Temperatures (in degrees Fahrenheit) 96 4 96 7 8 97 2 2 4 97 6 7 7 8 8 8 9 9 9 98 0 0 0 0 0 1 2 2 2 2 2 2 3 3 3 4 4 4 4 4 98 5 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9 99 0 0 1 1 2 2 3 4 99 9 100 0 100 8 Key 96 4 96 4 In an article in the Journal of Statistics Education (vol 4 no 2), 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 adult humans is 98 6 o F In his article, Shoemaker uses the data from the JAMA article to test this hypothesis Here is a summary of his test Claim The body temperature of adults is 98 6 o F Ho 98 6 o F Ha 98 6 o F Sample Size n 130 Population Adult Human Body Temperatures (measured in degrees Fahrenheit) (Data for the JAMA article were collected from healthy men and women, aged 18 to 40, at the University of Maryland Center for Vaccine Development, Baltimore) Data is presented in two stem and leaf charts at the end of this document and should be used to answer the questions below PLEASE USE ALL THE DATA IN THE STEM AND LEAF PLOTS, MALE AND FEMALE, FOR THESE QUESTIONS PLEASE UTILIZE BOTH STEM AND LEAF PLOTS IN YOUR ANALYSIS MALE AND FEMALE TEMERATURES FOR EXAMPLE, WHEN FINDING THE SAMPLE AVERAGE PLEASE INCLUDE BOTH SETS OF DATA IN YOUR COMPUTATION ALSO, PLEASE SKETCH HOW THE SAMPLING DISTRIBUTION WOULD LOOK I E QUESTION 1 Exercises 1 Complete the hypothesis test for all adults (men and women) by performing the following steps Use a level of significance of 05 Sketch the sampling distribution What is the value that you will place in the center Is the sampling distribution better represented by a t distribution or a normal distribution Why Is this hypothesis test set up as a two tail test or a one tail test Provide evidence to support your answer Is the sample size large enough to complete the hypothesis test Provide justification Compute the sample average, Compute the sample standard deviation, Compute the standard error of the distribution Using your sampling distribution, convert the sample average to a standardized test statistic, i e (t score or z score) Remember these scores represent the number of standard deviations the statistic (here the sample average) is from the center of the distribution Place the standardized test statistic on the sketch you drew above, as accurately as possible Does the standardized test statistic seem to be unusual In other words is it far away from the center of the distribution, which represents the null hypothesis claim (k) Compute the p value associated with your test statistic Remember you must use the alternative hypothesis to assist you in identifying the area that represents the p value (Show the commands you used on the calculator to perform this step You might also want to draw a sketch) (l) Make a decision to reject or fail to reject the null hypothesis Remember you must use your alpha value of 05 (m) Interpret the decision in the context of the original claim 2 If you lower the level of significance to 01 does your decision change Explain your reasoning 3 Use the sample of 130 temperatures to form a 99 confidence interval for the mean human body temperature of adult humans Does the value of 98 6 degrees fall in the confidence interval 4 The conventional normal body temperature was established by Carl Wunderlich over 100 years ago What, in Wunderlichs sampling procedure, do you think might have led him to an incorrect conclusion

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FOR THIS PROBLEM PLEASE USE ALL THE DATA - BOTH MEN AND WOMEN'S TEMPERATURES. Mens Temperatures (in degrees Fahrenheit) 96|3 97|7 9 97|0 1 1

FOR THIS PROBLEM PLEASE USE ALL THE DATA - BOTH MEN AND WOMEN'S TEMPERATURES.

Mens Temperatures

(in degrees Fahrenheit)

96|3

97|7 9

97|0 1 1 1 2 3 4 4 4 4

97|5 5 6 6 6 7 8 8 8 8 9 9

98|0 0 0 0 0 0 1 1 2 2 2 2 3 3 4 4 4 4

98|5 5 6 6 6 6 6 6 7 7 8 8 8 9

99|0 0 0 1 2 3 4

99|5

100|

Key:96|3 = 96.3

Womens Temperatures

(in degrees Fahrenheit)

96|4

96|7 8

97|2 2 4

97|6 7 7 8 8 8 9 9 9

98|0 0 0 0 0 1 2 2 2 2 2 2 3 3 3 4 4 4 4 4

98|5 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9

99|0 0 1 1 2 2 3 4

99|9

100|0

100|8

Key:96|4 = 96.4

In an article in the Journal of Statistics Education (vol.4 no. 2), 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 adult humans is 98.6^o F. In his article, Shoemaker uses the data from the JAMA article to test this hypothesis. Here is a summary of his test.

Claim: The body temperature of adults is 98.6^o F

Ho: =98.6^o F Ha: 98.6^o F

Sample Size: n = 130

Population: Adult Human Body Temperatures (measured in degrees Fahrenheit)

(Data for the JAMA article were collected from healthy men and women, aged 18 to 40, at the University of Maryland Center for Vaccine Development, Baltimore). Data is presented in two stem and leaf charts at the end of this document and should be used to answer the questions below.

PLEASE USE ALL THE DATA IN THE STEM AND LEAF PLOTS, MALE AND FEMALE, FOR THESE QUESTIONS

PLEASE UTILIZE BOTH STEM AND LEAF PLOTS IN YOUR ANALYSIS - MALE AND FEMALE TEMERATURES. FOR EXAMPLE, WHEN FINDING THE SAMPLE AVERAGE PLEASE INCLUDE BOTH SETS OF DATA IN YOUR COMPUTATION.

ALSO, PLEASE SKETCH HOW THE SAMPLING DISTRIBUTION WOULD LOOK I.E. QUESTION 1

Exercises

1. Complete the hypothesis test for all adults (men and women) by performing the following steps. Use a level of significance of .05

Sketch the sampling distribution.
1. What is the value that you will place in the center?

Is the sampling distribution better represented by a t-distribution or a normal distribution? Why?

Is this hypothesis test set up as a two tail test or a one tail test?
1. Provide evidence to support your answer.

Is the sample size large enough to complete the hypothesis test?
1. Provide justification.

Compute the sample average,

Compute the sample standard deviation,

Compute the standard error of the distribution;

Using your sampling distribution, convert the sample average to a standardized test statistic, i.e. (t-score or z-score) . Remember these scores represent the number of standard deviations the statistic (here the sample average) is from the center of the distribution

Place the standardized test statistic on the sketch you drew above, as accurately as possible.

Does the standardized test statistic seem to be unusual? In other words is it far away from the center of the distribution, which represents the null hypothesis claim.

(k) Compute the p-value associated with your test statistic. Remember you must use the alternative hypothesis to assist you in identifying the area that represents the p-value. (Show the commands you used on the calculator to perform this step. You might also want to draw a sketch).

(l) Make a decision to reject or fail to reject the null hypothesis. Remember you must use your alpha value of .05.

(m) Interpret the decision in the context of the original claim.

2. If you lower the level of significance to .01 does your decision change? Explain your reasoning?

3. Use the sample of 130 temperatures to form a 99% confidence interval for the mean human body temperature of adult humans. Does the value of 98.6 degrees fall in the confidence interval?

4. The conventional normal body temperature was established by Carl Wunderlich over 100 years ago. What, in Wunderlichs sampling procedure, do you think might have led him to an incorrect conclusion?