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 111.8 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          106.0

2          104.9

3          106.0

4          106.1

5          106.1

6          105.3

7          107.9

8          104.9

9          105.8

10        105.0

11        104.5

12        105.9

13        105.8

14        107.9

15        106.2

16        105.5

17        105.5

18        106.6

19        103.6

20        106.3

21        106.6

22        105.4

23        105.9

24        105.7

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, ?, pronounced as "alpha".

Select one:

a. ? = 5%, H1: ? > 111.8°F, H1: ? = 111.8°F

b. H1: ? = 111.8°F, ? = 2.5%, H1: ? ? 111.8°F

c. H0: ? ? 111.8°F, H1: ? = 111.8°F, ? = 10%

d. ? = 2.5%, H1: ? > 111.8°F, H0: ? = 111.8°F

Answer 1

You are given that the data is one tailed test and right tailed

Since the statement given as 'an electric fan is greater than 111.8 degrees Fahrenheit (°F) and you set the level of significance at 2.5% for your formal hypothesis test'.

So

Null hypotheses(H0) : $\mu$ = 111.8

Alternative hypotheses(H1) : $\mu$ > 111.8

And alpha level is 2.5%

Therefore

suitable option is 'D'