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 68.1 degrees Fahrenheit (°F) and you set the level of significance at 5% for your formal hypothesis test. You randomly sample 45 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) 1 111.6 2 111.9 3 110.0 4 109.7 5 110.3 6 109.1 7 109.1 8 111.2 9 111.2 10 109.9 11 110.7 12 109.6 13 110.9 14 109.4 15 108.6 16 110.7 17 109.6 18 110.7 19 110.4 20 111.1 21 110.7 22 111.5 23 110.8 24 110.3 25 111.9 26 109.9 27 109.4 28 111.2 29 109.4 30 108.8 31 109.7 32 109.3 33 110.2 34 111.2 35 110.9 36 109.4 37 110.0 38 110.3 39 112.1 40 108.8 41 108.3 42 110.4 43 110.3 44 110.7 45 111.6 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

Here we have to test the hypothesis that,

H0 : mu = 68.1 degrees or 154.58 Vs H1 : mu not= 68.1 degrees or 154.58

where mu is population mean temperature.

Assume alpha = level of significance = 0.05

Here we have given sample data so we use one sample t-test.

We can do one sample t-test in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Basic statistics --> 1-Sample t for the Mean --> Select data column --> Perform hypothesis test --> Hypothesized mean : 154.58 --> Options --> Confidence level : 95.0 --> Alternative : not= --> ok --> ok

————— 19-06-2018 11:16:38 ————————————————————

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One-Sample T: C1

Test of ? = 154.58 vs ? 154.58

Variable N Mean StDev SE Mean 95% CI T P
C1 45 110.387 1.282 0.191 (110.001, 110.772) -231.19 0.000

Test statistic = -231.19

P-value = 0.0000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the true population average core body temperature amidst higher ambient temperature and humidity levels while using an electric fan is different than 68.1 degrees Fahrenheit (°F).