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 214214 students. Can we conclude that freshman housing location and academic performance are related?

Location	Average	Below Average	Above Average	Total
On campus	7777	4242	3939	158158
Off campus	2828	1414	1414	5656
Total	105105	5656	5353	214214

Copy Data

Step 6 of 8 :  

Find the critical value of the test at the 0.0250.025 level of significance. Round your answer to three decimal places.

Step 7 of 8 : Make the decision to reject or fail to reject the null hypothesis at the

0.025

0.025

level of significance.

Step 8 of 8 : State the conclusion of the hypothesis test at the

0.025

0.025

level of significance.

Answer 1

(6) critical value=chi-square(0.025,2)=7.378 ( using ms-excel==CHIINV(0.025,2))

(7) since the critical value 7.378 is more than calcuated or obsersed chi-square=5.528 , so we fail to reject or accept null hypothesis at level of significance=0.025

(8) since we fail to reject null hypothesis , therefore we conclude that There is no relationship between freshman housing location and academic performance

followings are in details about the above answer

here we use chi-square test for independence of attributes with

null hypothesis H0: There is no relationship between freshman housing location and academic performance

alternate hypothesis Ha: There is no relationship between freshman housing location and academic performance

and chi-square=sum((O-E)2/E)= 5.528 with degree of freedom (r-1)(c-1)=(2-1)*(3-1)=2

following information has been generated using ms-excel

	Observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	7777	15958*10605/21614	7829.86	-52.8598	0.356859
	4242	15958*5656/21614	4175.925	66.07477	1.045487
	3939	15958*5353/21614	3952.215	-13.215	0.044187
	2828	5656*10605/21614	2775.14	52.85981	1.006854
	1414	5656*5656/21614	1480.075	-66.0748	2.949766
	1414	5656*5353/21614	1400.785	13.21495	0.124669
sum=	21614		21614	2.27E-13	5.527822