Question

1. 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 64.8 degrees Fahrenheit (°F) and you set the level of significance at 2.5% for your formal hypothesis test. You randomly sample 24 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	108.9
2	108.1
3	107.3
4	107.2
5	108.8
6	109.7
7	107.7
8	107.9
9	108.2
10	107.8
11	108.2
12	109.2
13	107.8
14	108.4
15	108.7
16	108.6
17	108.1
18	107.5
19	108.0
20	108.2
21	108.8
22	107.7
23	107.8
24	107.7

Per Step 1 of the 5-Steps to Hypothesis Testing, choose the appropriate null and alternative hypotheses, i.e. H0 and H1, respectively, as well as the significance level, α, pronounced as "alpha".

Select one:

a. H1: μ ≠ 64.8°F, α = 1%, H0: μ = 64.8°F

b. H1: μ > 64.8°F, α = 2.5%, H0: μ = 64.8°F

c. α = 10%, H0: μ < 64.8°F, H1: μ = 64.8°F

d. H0: μ < 64.8°F, H0: μ = 64.8°F, α = 5%

6. 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 proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 39.8% and setting the level of significance at 1% for the formal hypothesis test. You randomly sample 37 participants based on your research funding and for 45 minutes, the study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. At the end of the 45 minutes, you record for all participants if his/her heart and core temperature increased as compared to the start of the time period. The following table comprises the data you collect.

Subject	Heart and Core Temperature Increased?
1	0
2	0
3	0
4	1
5	0
6	1
7	1
8	1
9	1
10	1
11	0
12	1
13	1
14	0
15	0
16	0
17	0
18	1
19	0
20	1
21	1
22	1
23	0
24	0
25	0
26	0
27	0
28	0
29	1
30	0
31	0
32	1
33	0
34	1
35	0
36	1
37	0

Per Step 1 of the 5-Steps to Hypothesis Testing, choose the appropriate null and alternative hypotheses, i.e. H₀ and H₁, respectively, as well as the significance level, α, pronounced as "alpha".

Please note that 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health.

Select one:

a. α = 1%, H₀: p = 0.398, H₁: p < 0.398

b. H₀: p = 0.398, H₁: p ≠ 0.398, α = 10%

c. α = 5%, H₀: p < 0.398, H₁: p = 0.398

d. H₀: p ≠ 0.398, H₁: p = 0.398, α = 10%

Answer 1

1.

Claim - The true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is greater than 64.8 degrees Fahrenheit (°F). Thus the alternative hypothesis is H1: μ > 64.8°F. The null hypothesis will be H0: μ = 64.8°F

The level of significance at 2.5% .

The answer is,

b. H1: μ > 64.8°F, α = 2.5%, H0: μ = 64.8°F

2.

Claim - The true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 39.8%

Thus the alternative hypothesis is H1: p < 0.398. The null hypothesis will be H0: p = 0.398

The level of significance at 1% .

The answer is,

a. α = 1%, H0: p = 0.398, H1: p < 0.398