Sometimes when you are sick, your forehead feels really warm. You might have fever. How can you find out whether you do? By taking your temperature , of course. But what temperature should the thermometer show if your're healthy? Is this temperature the same for everyone? Several years ago, researchers conducted a study to determine whether the "accepted" value for normal body temperature, 98.6oF, 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 98.6oF was added for reference.
Do You Have a Fever?
Sometimes when you are sick, your forehead feels really warm. You might have fever. How can you find out whether you do? By taking your temperature , of course. But what temperature should the thermometer show if your're healthy? Is this temperature the same for everyone?
Several years ago, researchers conducted a study to determine whether the "accepted" value for normal body temperature, 98.6oF, 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 98.6oF was added for reference.
Statcrunch Data Link (Links to an external site.)
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 98.6oF.
If "normal" body temperature really is 98.6oF, we would expect that about half of all healthy 18- to 40-year-olds will have a body temperature less than 98.6oF. Do the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case?
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- What type of significance test would you run given the data above?
- What conditions must be satisfied for the test you have chosen in order to get valid results? Are the conditions satisfied?
- Run your test for significance using the data link above. Attach the data output including the hypotheses that you have chosen.
- Using the p-value (or critical values & test statistic), draw a proper conclusion and write said conclusion in context.
- Based on your conclusion, which type of error could have been made: a Type I error or a Type II error. Justify your answer.
- If you were a researcher, what type of data would you be interested in collecting? What would your null and alternative hypotheses be?
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- 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.
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