Question

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 41% and setting the level of significance at 1% for the 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 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	1
2	0
3	0
4	1
5	1
6	0
7	0
8	1
9	0
10	1
11	0
12	1
13	0
14	1
15	1
16	0
17	1
18	1
19	0
20	1
21	1
22	0
23	0
24	0
25	1
26	0
27	1
28	1
29	0
30	0
31	1
32	0
33	0
34	1
35	0
36	0
37	0
38	1
39	1
40	1
41	1
42	0
43	1
44	1
45	1
46	0
47	0
48	0
49	1
50	0

Per Step 5 of the 5-Steps to Hypothesis Testing, choose the appropriate formal and informal conclusions.

Please note the following: 1) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) in the prior question you already calculated a test statistic but on a different dataset – calculate the test statistic again using the dataset directly above in selecting the corresponding formal and informal conclusions.

Select one:

a. We do not accept H0 because z > -1.960, where z = 1.294. We have statistically significant evidence at ? = 5% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 41%.

b. We do not reject H1 because z ? +1.282, where z = 1.294. We have statistically significant evidence at ? = 5% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 41%.

c. We do not accept H1 because z = +1.645, where z = 1.294. We do not have statistically significant evidence at ? = 1% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 41%.

d. We do not reject H0 because z > -2.326, where z = 1.294. We do not have statistically significant evidence at ? = 1% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 41%.

Answer 1

For the given data we have:

Sample proportion, p = 25/50 = 0.5

Sample size, n = 50

Standard Error, SE = ((p*(1-p))/n)^0.5 = ((0.5*(1-0.5))/50)^0.5 = 0.0707

Test statistic, z = (p-0.41)/SE = (0.5-0.41)/0.0707 = 1.294

The critical z-score for a 1% significance level is:

z_c = -2.32

So the correct answer is:

We do not reject H₀ because z > -2.326, where z = 1.294. We do not have statistically significant evidence at ? = 1% to show that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels is less than 41%.

Hope this helps !