SOLUTION: Stan, please explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence. Please provide an example of using one of

Question 139460: Stan, please explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence. Please provide an example of using one of these hypothesis test. Please be specifc providing the steps to the hypothesis test in your exmaple.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence. Please provide an example of using one of these hypothesis test. Please be specifc providing the steps to the hypothesis test in your exmaple.
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These are large topics. You would have to see a text on statistics or use
Google to get all of what you are looking for. But here is a little of it.
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Goodness of Fit with a simplified example:
30 horse races are run with horses in 3 lanes.
# of wins from lane DISABLED_event_one= 8
# of wins from lane two = 12
# of wins from lane three = 10
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Ho: It makes no difference which lane the horse starts in.
Ha: It makes a difference.
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Comment: If it makes no difference there should be 10 wins from each position.
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Run a Chi-Sq on a 2 x 3 Matrix:
row 1: 8....12....10
row 2: 10...10....10
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Chi-Sq results:
Test statistic: Chi-Sq = 0.404040404...
p-value: 0.81707
df=2
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Conclusion: Since p-value is greater than 5%, Fail to reject Ho.
It makes no difference which lane the horse starts in.
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Ch-Sq Test for Independence
You have three horses, A, B, C and you have three lanes on the track 1,2.3.
You keep track of how many wins each horse has on each track.
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------------------A..........B........C
row 1.............2..........4........3
row 2.............3..........5........1
row 3.............4..........2........5
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Ho: Horses and lanes are independent
Ha: They are dependent
Run a Chi-Sq on the 3 x 3 Matrix and get the following
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Test Statistic: Chi-Sq = 0.213447...
p-value = 0.37789..
df=4
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Conclusion: Since p-value is greater than 5%, Fail to reject Ho.
Horses and lanes are independent.
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Hope that helps.
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Cheers,
Stan H.
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