Question

1. The National Assessment of Educational Progress (NAEP) is an assessment of student learning that involves samples of students from every state. Scores are reported in four performance categories: Below Basic, Basic, Proficient, and Advanced. A researcher wanted to know if there was a relationship between state of residence and performance on NAEP. The researcher obtained the following data from the NAEP website. (You do not have to do follow up procedure.)
   

State	Below Basic	Basic	Proficient	Advanced
VA	360	1200	1140	270
SC	609	1276	870	145
NC	572	1848	1628	352

Use the chi-square test to determine if there is relationship between state of residence and NAEP performance level? Write a short summary of your results. Be sure to include the appropriate statistical evidence: test statistic used, degrees of freedom, value of the test statistic, and test statistic critical value. Use α = .05.

Answer 1

Ans:

Chi square test for independence:

	Observed(fo)
State	Below Basic	Basic	Proficient	Advanced	Total
VA	360	1200	1140	270	2970
SC	609	1276	870	145	2900
NC	572	1848	1628	352	4400
Total	1541	4324	3638	767	10270
	Expected(fe)
State	Below Basic	Basic	Proficient	Advanced	Total
VA	445.64	1250.47	1052.08	221.81	2970
SC	435.14	1220.99	1027.28	216.58	2900
NC	660.21	1852.54	1558.64	328.61	4400
Total	1541	4324	3638	767	10270
	Chi square=(fo-fe)^2/fe
State	Below Basic	Basic	Proficient	Advanced	Total
VA	16.46	2.04	7.35	10.47	36.31
SC	69.46	2.48	24.08	23.66	119.68
NC	11.79	0.01	3.09	1.67	16.55
Total	97.71	4.53	34.52	35.79	172.54

Chi square

Test statistic:=172.54

degree of freedom=(3-1)*(4-1)=6

Critical chi square=CHIINV(0.05,6)=12.592

p-value=CHIDIST(172.54,6)=0.0000