1. Comparison of Two Means Paul Niezguski Peter Heisler University of Michigan College of Engineering

2. Professor X is curious if there is statistical difference between the test grades of his morning and afternoon chemistry classes

3. Statistical data for the two classes: Morning class:Afternoon class: mean:78.5mean:84.2 std. dev:11.3std. dev:11.0 sample size:24sample size:27

4. He hypothesizes that afternoon students will be more alert in class and thus have higher test scores. The class test means support this, but to what certainty can Professor X make this assertion?

5. He finds a wiki article on comparison of means by using the Student’s t test. This method uses the following equations: x 1 = mean from data set 1 x 2 = mean from data set 2 n 1 = number of measurements set 1 n 2 = number of measurements set 2 s 1 = std. deviation of set 1 s 2 = std. deviation of set 2 For two sets with similar standard deviations:

6. After a careful mental calculation by professor X, he determines the following t value: t = 1.820741

7. He then consults the following t table to determine at what confidence level the means are statistically different:

8. The table gives a confidence level of 90 – 95% that the two means are statistically different…thus Professor X’s hypothesis is most likely correct. He is so pleased he decides to go hunting.

9. THE END