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 105.6 degrees Fahrenheit (°F) and you set the level of significance at 10% for your formal hypothesis test. You randomly sample 39 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) 1 110.2 2 109.8 3 109.7 4 109.7 5 110.7 6 110.6 7 109.8 8 110.6 9 110.6 10 109.7 11 110.8 12 109.8 13 110.5 14 108.0 15 110.9 16 109.8 17 110.6 18 112.0 19 110.4 20 109.8 21 111.3 22 110.6 23 110.2 24 110.4 25 109.8 26 111.2 27 110.1 28 109.6 29 110.4 30 110.3 31 110.5 32 111.5 33 109.9 34 110.9 35 111.5 36 110.5 37 110.7 38 110.6 39 111.9 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 1

Solution:

Here, we have to use one sample t test for population mean. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is 105.6 degrees Fahrenheit (°F).

Alternative hypothesis: H_a: The true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 105.6 degrees Fahrenheit (°F).

H₀: µ = 105.6 versus H_a: µ ? 105.6

This is a two tailed test.

We are given level of significance = ? = 10% = 0.10

From given sample data for core body temperatures, we have

Sample mean = Xbar = 110.4076923

Sample standard deviation = S = 0.729954799

Sample size = n = 39

Degrees of freedom = n – 1 = 39 – 1 = 38

Now, we have to find critical values by using t-table.

Lower critical value = -1.6860

Upper critical value = 1.6860

(For two tailed test, there are two critical values.)

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (110.4076923 – 105.6) / [0.729954799 / sqrt(39)]

t = (110.4076923 – 105.6) /0.1169

t = 41.1314

P-value = 0.0000

? = 0.10

P-value < ?

So, we reject the null hypothesis that true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is 105.6 degrees Fahrenheit (°F).

There is sufficient evidence to conclude that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 105.6 degrees Fahrenheit (°F).