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 86 degrees Fahrenheit (°F) and you set the level of significance at 5% 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	99.9
2	98.0
3	99.1
4	98.6
5	99.7
6	98.1
7	98.6
8	97.8
9	99.0
10	98.0
11	98.9
12	100.3
13	99.0
14	98.0
15	98.5
16	99.3
17	98.2
18	98.0
19	99.4
20	99.1
21	97.5
22	98.3
23	100.0
24	98.7
25	99.1
26	98.1
27	97.6
28	101.0
29	98.3
30	98.9
31	98.4
32	97.0
33	98.4
34	100.1
35	99.1
36	99.2
37	97.6
38	99.3
39	97.6
40	98.4
41	100.4
42	98.9
43	98.1
44	99.0
45	97.5
46	100.0
47	98.6
48	100.3
49	97.9

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:

Answer 1

As Population variance is notknown we use one sample t test.

Below is the output from excel

t-Test: One-Sample
	Temperature (°F)
Mean	98.75102041
Variance	0.796717687
Observations	49
Hypothesized Mean Difference	86
df	48
t Stat	99.99787049
P(T<=t) one-tail	1.14643E-57
t Critical one-tail	1.677224196
P(T<=t) two-tail	2.29285E-57
t Critical two-tail	2.010634758

The test statistic value is 99.99787049

Test statistic follows t distribution with n-1 = 48 degree of freedom.

Rejection Rule: Reject H0 if |t_cal| > t_critical

t_critical = 2.010634758 (As our test is 2 tail test)

p-value = 2.29285E-57

as p_value is less than 0.05 (l.o.s) we reject H0 at 5% l.o.s

Hence, there is sufficient evidence to say that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 86 degrees Fahrenheit (°F)