Question

Recently, California has pushed for a new ethnic studies graduation requirement for high schoolers and students of the California State University system, AB 331. A sociologist suggests support for the proposed legislation is largely divided by racial groups. The following data table shows support for AB 331 based on the 5 racial groups designated by the U.S. Census. The scale is 1 to 7 where 1 represents no support and 7 represents complete support ----ANOVA method---

White	Black	Asian	Native American or Alaska Native	Native Hawaiian or Pacific Islander
1	5	4	1	5
2	4	2	4	6
7	4	1	2	6
3	4	5	4	7
2	3	4	2	7

Answer 1

treatment	w'hite	Black	Asian	Native American or Alaska Native	Native Hawaiian or Pacific Islander
count, ni =	5	5	5	5	5
mean , x̅ i =	3.000	4.00	3.20	2.60	6.200
std. dev., si =	2.3	0.7	1.6	1.3	0.8
sample variances, si^2 =	5.500	0.500	2.700	1.800	0.700
total sum	15	20	16	13	31		95	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =						3.80
( x̅ - x̅̅ )²	0.640	0.040	0.360	1.440	5.760
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	3.200	0.200	1.800	7.200	28.800		41.2
SS(within ) = SSW = Σ(n-1)s² =	22.000	2.000	10.800	7.200	2.800		44.8000

no. of treatment , k =   5  
df between = k-1 =    4  
N = Σn =   25  
df within = N-k =   20  
      
mean square between groups , MSB = SSB/k-1 =    41.2/4=   10.3000
mean square within groups , MSW = SSW/N-k =    44.8/20=   2.2400
      
F-stat = MSB/MSW =    10.3/2.24=   4.60

ANOVA
	SS	df	MS	F	p-value	F-critical
Between:	41.20	4	10.30	4.598	0.0085	2.8661
Within:	44.80	20	2.24
Total:	86.00	24
					α =	0.05

   Decision:   p-value<α , reject null hypothesis
      
conclusion :    there is enough evidence of significant mean difference among five  treatments