Question

An educational researcher wishes to know if there is a difference in academic performance for college freshmen that live on campus and those that commute. Data was collected from 267 students. Can we conclude that freshman housing location and academic performance are related? Location Average Below Average Above Average Total On campus 89 29 27 145 Off campus 36 43 43 122 Total 125 72 70 267 Copy Data Step 2 of 8 : Find the expected value for the number of students that live on campus and have academic performance that is average. Round your answer to one decimal place.

Answer 1

Ho:  there is no  difference in academic performance for college freshmen that live on campus and those that commute

H1:  there is a difference in academic performance for college freshmen that live on campus and those that commute

Chi-Square Test of independence
	Observed Frequencies
	Y
0	average	below average	above average				Total
on campus	89	29	27				145
off campus	36	43	43				122
Total	125	72	70				267
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	average	below average	above average				Total
on campus	125*145/267=67.884	72*145/267=39.101	70*145/267=38.015				145
off campus	125*122/267=57.116	72*122/267=32.899	70*122/267=31.985				122
Total	125	72	70				267
	(fo-fe)^2/fe
on campus	6.5684	2.6095	3.192
off campus	7.8067	3.1014	3.793

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   27.0710  
      
Number of Rows =   2  
Number of Columns =   3  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2  
      
p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho  

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the expected value for the number of students that live on campus and have academic performance that is average=125*145/267=67.9