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 different than 77.5 degrees Fahrenheit (°F) and you set the level of significance at 10% for your formal hypothesis test. You randomly sample 49 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	107.8
2	108.2
3	107.0
4	107.9
5	107.7
6	109.0
7	106.3
8	108.5
9	106.7
10	107.2
11	107.2
12	107.6
13	108.3
14	107.9
15	108.5
16	108.5
17	107.4
18	107.0
19	108.7
20	105.9
21	107.3
22	107.9
23	107.7
24	107.9
25	107.8
26	107.0
27	107.9
28	107.5
29	108.4
30	106.5
31	107.9
32	107.5
33	108.0
34	108.7
35	108.4
36	107.5
37	107.8
38	107.7
39	107.3
40	107.6
41	108.0
42	107.2
43	109.2
44	107.6
45	106.8
46	107.9
47	107.7
48	108.0
49	106.6

Per Step 5 of the 5-Steps to Hypothesis Testing, choose the appropriate formal and informal conclusions.

Please note the following: 1) you may copy and paste the data into Excel to facilitate analysis; and 2) in the prior question you already calculated a test statistic but on a different dataset – calculate the test statistic again using the dataset directly above in selecting the corresponding formal and informal conclusions.

Select one:

a. We do not reject H₀ because z ≤ +1.960 or z < +1.282, where z = 308.898. We do not have statistically significant evidence at α = 1% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is different than 77.5°F.

b. We do not accept H₁ because z > -1.960 and z > -1.645, where z = 308.898. We do not have statistically significant evidence at α = 2.5% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is different than 77.5°F.

c. We reject H₀ because z ≤ -1.645 or z ≥ +1.645, where z = 308.898. We have statistically significant evidence at α = 10% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 77.5°F.

d. We do not reject H₀ because z ≤ +1.960 and z = -1.960, where z = 308.898. We do not have statistically significant evidence at α = 2.5% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is different than 77.5°F.

Answer 1

Sample mean using excel function AVERAGE(), x̅ = 107.6857

Sample standard deviation using excel function STDEV.S, s = 0.684044

Sample size, n = 49

Null and Alternative hypothesis:

Ho : µ = 77.5 ; H1 : µ ≠ 77.5

Critical value, z crit = ABS(NORM.S.INV(0.1/2)) = 1.645

Reject Ho if z < -1.645 or if z > 1.645

Test statistic:

z = (x̅- µ)/(s/√n) = (107.6857 - 77.5)/(0.684/√49) = 308.898

Decision:

Reject the null hypothesis

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Answer:

C. We reject H₀ because z ≤ -1.645 or z ≥ +1.645, where z = 308.898. We have statistically significant evidence at α = 10% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 77.5°F.