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 greater than 107.1 degrees Fahrenheit (°F) and you set the level of significance at 1% for your formal hypothesis test. You randomly sample 26 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) 1 108.6 2 109.2 3 108.1 4 108.0 5 109.2 6 109.3 7 110.0 8 109.1 9 108.3 10 109.3 11 110.0 12 109.3 13 107.5 14 108.9 15 109.3 16 108.4 17 108.6 18 109.3 19 109.2 20 108.3 21 109.0 22 110.1 23 109.0 24 110.9 25 108.8 26 109.5 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:

Answer 1

Given,

Sample size, n = 26

Sample mean, $\bar{x}$ = $\frac{\sum x_{i}}{n}$ = 109.046

Sample standard deviation,s = $\sqrt{\frac{(\sum x_{i} - \bar{x})^{2}}{n-1}}$ = 0.731

Where x_i is the each observation, i = 1,2,3- - - , 26.

Degree of freedom = n-1 = 26-1 = 25

Level of significance = 1% = 0.01

Hypthesis:

Let the null and alternative hypothesis be:

H₀ : $\mu$ $\leq$ 107.1

H₁ : $\mu >$ 107.1 (Right tailed)

Where $\mu$ is the True population average core body temperature.

Test Statistic:

We will use t-test here, as n < 30 and population standard deviation is not given.

$t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{109.046-107.1}{\frac{0.731}{\sqrt{26}}}$

t = 13.574   

Decision Rule:

t-critical value = 2.485 (For right tailed) (Degree of freedom = 25)

(By using t-table at 0.01 level of significance)

We will reject the null hypothesis for right tailed distribution, if t(caculated) > t(critical).

Result:

Here, t(calculated) = 13.574

So, t(calculted) > t(critical)

Hence, we reject the null hypothesis.

Conclusion:

At 0.01 or 1% level of significance using given sample information there are sufficient evidence to claim that "the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is greater than 107.1 degrees Fahrenheit (°F)."