Question

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13. 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 90.1 degrees Fahrenheit (°F) and you set the level of significance at 2.5% for your formal hypothesis test. You randomly sample 50 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 45minute 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	108.8
2	109.0
3	110.3
4	108.6
5	110.3
6	109.0
7	107.7
8	109.1
9	107.9
10	108.7
11	108.1
12	109.3
13	109.6
14	109.5
15	109.3
16	109.9
17	108.6
18	110.3
19	109.5
20	108.9
21	108.5
22	110.0
23	110.5
24	110.0
25	108.6
26	109.9
27	110.4
28	110.9
29	109.7
30	108.2
31	108.8
32	109.7
33	108.6
34	109.8
35	111.4
36	109.0
37	108.8
38	109.1
39	108.9
40	108.1
41	108.3
42	109.8
43	110.4
44	110.9
45	107.9
46	111.6
47	109.5
48	109.1
49	108.7
50	109.2

Per Step 3 of the 5-Steps to Hypothesis Testing, choose the appropriate decision rule.

Select one:

a. Reject H₀ if z = +2.576 and z > -2.241

b. Reject H₀ if t = -1.960 and t < -1.960

c. Accept H₁ if z ≤ -1.645 or t ≥ +1.645

d. Reject H₀ if z ≤ -2.241 or z ≥ +2.241

Answer 1

d. Reject H₀ if z ≤ -2.241 or z ≥ +2.241

Level of Significance ,    α =    0.025

Tail = 2

critical z value, z* =   ±   2.2414   [Excel formula =NORMSINV(α/no. of tails) ]  

Ho :   µ =   90.1                  
Ha :   µ ╪   90.1       (Two tail test)          
                          
Level of Significance ,    α =    0.03                  
population std dev ,    σ =    0.9115                  
Sample Size ,   n =    50                  
Sample Mean,    x̅ = ΣX/n =    109.3340                  
                          
  
                          
Standard Error , SE = σ/√n =   0.9115   / √    50   =   0.1289      
Z-test statistic= (x̅ - µ )/SE = (   109.334   -   90.1   ) /    0.1289   =   149.21
                          
critical z value, z* =   ±   2.2414   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
p-Value   =   0.0000   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value<α, Reject null hypothesis                       

       

THANKS

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