365, 5280, 98.6.
These are numbers that we all learned from a very young age. Number of days in a year, number of feet in a mile, and normal body temperature. This last number, the normal body temperature, comes from the research of a German physician in the 1800s. Recent research suggests this is all wrong. Of course, we thought it would be fun to design a new lesson to be able to come to our own conclusion.
Learning Targets
Perform a significance test for a mean.
Use a confidence interval to make a conclusion for a two-sided test about a population mean.
First things first, we had to find an accurate and efficient way to measure body temperature. A quick visit to the AP Biology teacher and we had a solution: a forehead thermometer. In class, we asked for one student volunteer to be the physician, and one to record the data. We were able to collect body temperatures for all student in class in less than 10 minutes. We used this applet to quickly analyze the data.
What About the Conditions?
Because we are using all students in class, the Random condition is not satisfied. But, we feel comfortable that our class of students will be representative of the population of all students at East Kentwood High School, and so it still makes sense to do inference. Also, if you have classes with less than 30 students, you might end up with an outlier in the sample data, and the Normal condition might be at risk. You will notice in the lesson that we went with "assume all conditions" have been met.
Wait, Confidence Intervals and Significance Tests are Related?
At this point in the year, students are very comfortable using a confidence interval to evaluate a claim (based on your confidence interval, is there convincing evidence that....) But what many of them didn't realize until this lesson was the close connection between the confidence level for a confidence interval and the significance level, alpha, for a significance test.
If the null hypothesis value is NOT contained within the 95% confidence interval, then this value for the parameter is not plausible, and we reject the null at alpha = 0.05 for a two-sided test.
If the null hypothesis value is contained within the 95% confidence interval, then this value for the parameter is plausible, and we fail to reject the null at alpha = 0.05 for a two-sided test.
More generally: Confidence level = 1 - alpha
Final note: in all four of our classes, we found convincing evidence that 98.6 degrees Fahrenheit is no longer the "normal" body temperature.
Activity: What is Normal Body Temperature?
Answer Key: PDF