Question

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 10% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 44 and 15 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all 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%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only 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, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans Subject Core Body Temperature Increased? 1 0 2 1 3 0 4 0 5 0 6 0 7 0 8 1 9 0 10 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 0 26 0 27 1 28 0 29 0 30 1 31 1 32 0 33 0 34 0 35 0 36 0 37 1 38 0 39 0 40 0 41 1 42 0 43 0 44 0

Table 2. Fans Subject Core Body Temperature Increased? 1 0 2 1 3 0 4 0 5 0 6 1 7 1 8 1 9 0 10 0 11 0 12 0 13 0 14 1 15 0

Per Steps 4 and 5 of the 5-Steps to Hypothesis Testing, compute the test statistic using the appropriate test statistic formula and 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) 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 1

For sample 1, we have that the sample size is N 44, the number of favorable cases is X7, so then the sample proportion is pl #-П-0.1591 For sample 2, we have that the sample size is No :-15, the number of favorable cases is X2 5, so then the sample proportion is p0.3333 The value of the pooled proportion is computed as p = N-# 0.2034 Also, the given significance level is α-0.1 The following null and alternative hypotheses need to be tested Ho pP2 This corresponds to a left-tailed test, for which a z-test for two population proportions needs to be conducted (2) Rejection Region Based on the information provided, the significance level is 0.1, and the critical value for a left tailed test is c1.28 The rejection region for this left-tailed test is R z-1.28 The z-statistic is computed as follows 0.1591- 0.3333 Vp1 (1/ni +1/n2) V0.2034 (1 0.2034) (1/44+ +1/15 1.448 Since it is observed that z1.4481.28, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p 0.0738, and since p 0.07380.1, it is concluded that the null hypothesis is rejected It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion pi is less than p, at the 0.1 significance level