Question

Several years ago, researchers conducted a study to determine whether the "accepted" value for normal body temperature, 98.6^oF, is accurate. They used an oral thermometer to measure the temperatures of a random sample of healthy men and women aged 18 to 40. As is often the case, the researchers did not provide their original data.

Allen Shoemaker, from Calvin College, produced a data set with the same properties as the original temperature readings. His data set consists of one oral temperature reading for each of the 130 randomly chosen, healthy 18- to 40-year-olds. A dotplot of Shoemaker's temperature data is shown below. A vertical line at 98.6^oF was added for reference.

Exploratory data analysis revealed several interesting facts about this data set:

• The mean temperature was x ¯ = 98.25 o F
• The standard deviation of the temperature reading was s x = 0.73 o F
• 62.3% of the temperature readings were less than 98.6^oF.

If "normal" body temperature really is 98.6^oF, we would expect that about half of all healthy 18- to 40-year-olds will have a body temperature less than 98.6^oF. Do the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case?

1. What type of significance test would you run given the data above?
2. What conditions must be satisfied for the test you have chosen in order to get valid results? Are the conditions satisfied?
3. Run your test for significance using the data link above. Attach the data output including the hypotheses that you have chosen.
4. Using the p-value (or critical values & test statistic), draw a proper conclusion and write said conclusion in context.
5. Based on your conclusion, which type of error could have been made: a Type I error or a Type II error. Justify your answer.
6. If you were a researcher, what type of data would you be interested in collecting? What would your null and alternative hypotheses be?
   • For example: Just down from my house is a stop sign, in which most people roll through without fully stopping. My claim would be "most people fail to stop at the stop sign" with H₀: p = 0.50 and H₁: p > 0.50. I would watch at random times of the day and keep a tally of those who do make a full stop vs. those who roll through or fail to stop at all. My proportion would be the number of people who don't stop divided by the total observations I recorded.

Answer 1