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%

2. 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 58.7 degrees Fahrenheit (°F) and you set the level of significance at 2.5% for your formal hypothesis test. You randomly sample 15 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	109.6
2	110.8
3	109.9
4	110.2
5	110.3
6	109.2
7	110.3
8	110.0
9	111.7
10	109.5
11	110.3
12	110.5
13	110.1
14	109.2
15	110.9

Per Step 2 of the 5-Steps to Hypothesis Testing, choose the appropriate test statistic.

Select one:

a. z = (X̄ - µ₀) / (s / √n)

b. z = (p̂ - p₀) / √(p₀ * (1 - p₀) / n), where p̂ = x / n

c. z = (p̂₁ - p̂₂) / √[ p̂ * (1 - p̂) * (1 / n₁ + 1 / n₂) ], where p̂₁ = x₁ / n₁, p̂₂ = x₂ / n₂, p̂ = (x₁ + x₂) / (n₁ + n₂)

d. t = (X̄ - µ₀) / (s / √n)

Answer 1

1)

Answer:

Explanation:

The result from the previous study is used to define the null hypothesis such that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is 64.8 degrees Fahrenheit and the alternative hypothesis tests the claim made by the researcher such that this average is greater than 64.8 degrees Fahrenheit

This is a one-tailed test.

The significance level of the test = 2.5%

2)

Answer:

Explanation:

Since we are comparing the one sample mean with the hypothesized population mean and the population standard deviation is not known, the one-sample t-test will be used to test the hypothesis,

(we use one sample z test for mean when the population standard deviation is known and one-sample t-test for mean when the population standard deviation is not known)

The t-statistic is obtained using the following formula,