[Statistics] Obtaining test statistic in short problem

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The discussion revolves around calculating the test statistic for a statistical problem related to a sample of 120 people categorized as workers, students, and retirees. Participants debate whether to use an F-test or a chi-square statistic for analysis. The F-test formula is provided, emphasizing the importance of R-squared in determining model effectiveness. The conversation highlights the need to calculate expected counts in each category based on predicted percentages. Clarification is sought on how to derive these expected counts from the given data.
ozill
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Hey everyone! Exam practice, that time of year. In this problem 13 with correct answer C, I'm not sure how they get the test statistic: http://i.imgur.com/doar3.jpgI think they want you to use a F-test, that tests the entire model, which is calculated by: F= ((R^2)/ K)/ ((1 - R^2)/(n-K-1)) where K is the number of independent variables (3 in this question)

Then the R square is the percentage of the model that is explained, so the explained variation in Y / total variation in Y

R^2 = SSR / (SSE+SSR)
SSR= sum of squared regression, SSE=sum of squared errors

Thanks for any help or insight!
Many thanks
 
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I think they are doing a contingency table with a chi-square statistic.
 
Right, but I'm still at a loss! :)
 
Well, how many people in each of the three categories would expect, based on the predicted percentages? And how many were actually surveyed?
 
Hey, thanks for helping!

It's a sample of 120 people, so n=120
So in this sample : 60 workers, 30 students, 30 retirees
 
ozill said:
Hey, thanks for helping!

It's a sample of 120 people, so n=120
So in this sample : 60 workers, 30 students, 30 retirees

That was not the question. The question was: how many would you EXPECT in each group if the predicted percentages held true?

RGV
 

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