Question

Previous research states, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness. Counterintuitively, Public Health guidelines suggest not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to research further this seemingly contradictory guidance, hypothesizing that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is greater than 91.9 degrees Fahrenheit (°F) and you set the level of significance at 5% for your formal hypothesis test. You randomly sample 13 participants based on your research funding and for 45 minutes, the study participants sit in a chamber maintained at a temperature of 108°F (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45 minute warming period, for each participant you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes. At the end of this 45 minute fan period, you record the core body temperature of all participants. The following table comprises the data you collect.

Subject	Core Body Temperature (°F)
1	105.0
2	104.9
3	104.6
4	104.3
5	105.2
6	105.1
7	105.4
8	104.0
9	104.1
10	104.9
11	105.1
12	104.2
13	105.8

Per Step 4 of the 5-Steps to Hypothesis Testing, compute the test statistic using the appropriate test statistic formula.

Please note the following: 1) you may copy and paste the data into Excel to facilitate analysis and 2) do not round your numerical answer that you submit as the online grading system is designed to mark an answer correct if your response is within a given range. In other words, the system does not take into account rounding. On the other hand, rounding is preferable when formally reporting your statistical results to colleagues.

Answer 1

Given,

Sample size : n= 13

Hypothesized mean : = 91.9

x : Core Body temperature

Sample mean :

Sample standard deviation : s

Subject	x: Core Body temperature	x-xbar	x-xbar2
1	105	0.184615385	0.03408284
2	104.9	0.084615385	0.007159763
3	104.6	-0.215384615	0.046390533
4	104.3	-0.515384615	0.265621302
5	105.2	0.384615385	0.147928994
6	105.1	0.284615385	0.081005917
7	105.4	0.584615385	0.341775148
8	104	-0.815384615	0.664852071
9	104.1	-0.715384615	0.511775148
10	104.9	0.084615385	0.007159763
11	105.1	0.284615385	0.081005917
12	104.2	-0.615384615	0.378698225
13	105.8	0.984615385	0.969467456
Total	1362.6		3.536923077
Mean	1362.6/13= 104.8153846

Test Statistic = 85.7742315079451