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 dot plot of Shoemaker's temperature data is shown below. A vertical line at 98.6oF 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 98.6oF. 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? 1. Does the data provide convincing evidence that the true mean body temperature in all healthy 18-40 year-olds is not 98.6 F? 2. A 95% confidence interval for the population mean is 98.123 F to 98.377 F. Explain how the confidence interval is consistent with, but gives more information than, the significance test in the previous question.
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 dot plot of Shoemaker's temperature data is shown below. A vertical line at 98.6oF 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 98.6oF.
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?
1. Does the data provide convincing evidence that the true mean body temperature in all healthy 18-40 year-olds is not 98.6 F?
2. A 95% confidence interval for the population mean is 98.123 F to 98.377 F. Explain how the confidence interval is consistent with, but gives more information than, the significance test in the previous question.
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