Comparison of Two Means

Paul NiezguskiPeter Heisler

University of MichiganCollege of Engineering

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

Statistical data for the two classes:

Morning class: Afternoon class:mean: 78.5 mean: 84.2std. dev: 11.3 std. dev: 11.0sample size: 24 sample size: 27

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?

He finds a wiki article on comparison of means by using the Student’s t test.This method uses the following equations:

x1= mean from data set 1x2= mean from data set 2n1= number of measurements set 1n2= number of measurements set 2

s1 = std. deviation of set 1s2 = std. deviation of set 2

For two sets with similar standard deviations:

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

t = 1.820741

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

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.

THE END