You decide to research further this seemingly contradictory guidance, hypothesiz

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 greater than 23.6% and setting the level of significance at 10% for the formal hypothesis test. You randomly sample 37 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.

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) 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.

Subject Heart and Core
Temperature
Increased? 1 1 2 0 3 1 4 1 5 0 6 0 7 1 8 0 9 0 10 0 11 0 12 0 13 1 14 0 15 0 16 1 17 0 18 0 19 0 20 0 21 0 22 1 23 1 24 0 25 1 26 0 27 0 28 0 29 0 30 1 31 0 32 1 33 0 34 0 35 0 36 0 37 0

Explanation / Answer

Here the hypothesises are

Null Hypothesis : H0 : p = 0.236

ALternative Hypothesis : Ha : p > 0.236

where p is the true proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels.

HEre sample size n = 37

Sample proportion p^ = 11/37 = 0.2973 [ here 11 is total 1' s in the given list]

Here standard error of proportion = sqrt [p0 * ( 1- p0)/N] = sqrt [0.236 * (1 - 0.236)/37] = 0.0698

Here test statistic

Z = (p^ -p0)/sep = (0.2973 - 0.236)/ 0.0698 = 0.8781

p - value = Pr(Z > 0.8781) = 0.1900

so here p - vaalue > 0.10

so we will reject the null hypothesis and can conclude that the true population proportion of heart and core temperature increases amidst higher ambient temperature and humidity levels.

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