Download - Comparison of Two Means Paul Niezguski Peter Heisler University of Michigan College of Engineering
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Comparison of Two Means
Paul NiezguskiPeter Heisler
University of MichiganCollege of Engineering
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Professor X is curious if there is statistical difference between the test grades of his morning and afternoon chemistry classes
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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
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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?
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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:
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After a careful mental calculation by professor X, he determines the following t value:
t = 1.820741
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He then consults the following t table to determine at what confidence level the means are statistically different:
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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.
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THE END