The number of students enrolled into the Math Faculty, Art Faculty, and Environment Faculty of a university is shown as follow:
|
Math
|
Art
|
Environment
|
Row total
|
Male
|
250
|
120
|
180
|
550
|
Female
|
150
|
300
|
150
|
600
|
Column total
|
400
|
420
|
330
|
1150
|
|
|
Now we want to test if there is a difference between preferences towards these three faculties from male students to female students.
Notice: The matrix we build up for the test for this case should be
1.
|
Determine the null hypothesis:
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Null Hypothesis: Gender and preferences to these three faculties are independent.
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2.
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Compare the expected data and the observed data:
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Observed
|
Expected
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O[1,1] = 250
|
E[1,1] = = 191.30435
|
O[1,2] = 120
|
E[1,2] = = 200.86957
|
O[1,3] = 180
|
E[1,3] = = 157.82609
|
O[2,1] = 150
|
E[2,1] = = 208.69565
|
O[2,2] = 300
|
E[2,2] = = 219.13043
|
O[2,3] = 150
|
E[2,3] = = 172.17391
|
|
|
3.
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Substitute the information into the formula:
|
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x = = 102.891
|
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p-value = = 0 (a small value very close to 0)
|
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This statistical test provides evidence that the null hypothesis is false, so we reject the null hypothesis.
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