Question

Chi-square Goodness of Fit

In may 2002 the AP statistics exam was administered to a total of 48,790 students. The national grades and CLHS students grades are listed below.

National Scores

Score (5) (4) (3) (2) (1)

Percent (11.1) (21.6) (23.9) (19.2) (24.2)

CLHS Student Scores

Score (5) (4) (3) (2) (1)  

Students (16) (21) (11) (2) (0)

Is the distribution of scores for CLHS students significantly different from national scores?

Answer 1

Ho:  distribution of scores for CLHS students is not different from national scores

H1: distribution of scores for CLHS students is significantly different from national scores

Chi square test for Goodness of fit

expected frequncy,E = expected proportions*total frequency

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
5	16	0.111	5.55			19.676
4	21	0.216	10.8			9.633
3	11	0.239	11.95			0.076
2	2	0.192	9.6			6.017
1	0	0.242	12.1			12.100

	total frequency	(O-E)²/E
total sum ,Σ	50	47.502

level of significance, α=   0.05          
Degree of freedom=k-1=   5   -   1   4
  
              
chi square test statistic,X² = Σ(O-E)²/E =   47.502          
              
P value = 0.0000 [ excel function: =chisq.dist.rt(test-stat,df) ]      

since, p value < α, reject Ho,

hence, distribution of scores for CLHS students is significantly different from national scores at α=0.05