Question

1. Professor Seal selects a sample 3rd graders from each of three schools offering different programs in math. He wishes to determine whether there are differences between these schools in student calculation skills. Professor Seals tests each child in calculation ability and obtains these results (19 points) Phonological awareness scores Program 1 14.10.17.13 Program 2 5.7. 12.8 Program 3 | 18.9.15.16 1a. Give the H. (No more than 2 sentences): (2 points) 16. Compute SS with SS between and SStotal - You may use the attached table here to help organize your work. Fill in the blanks with your answers and show your statistical work. (5 points) Program 3 Program 1 (n=4) Values Program 2 (n =4) Values (x-M2 (x-M2 Values (x-M) 17 16 13 14 12 15 10 M1 = (x-M1) M = (x-M) M3 = (x-M3)

Answer 1

(1a) null hypothesis H0:$\mu$1=$\mu$2=$\mu$3

alternate hypothesis Ha: atleast one $\mu$ is different from others

(1b) here grand mean M=12 and total sum of square=SS_total=sum((x-12)²)=34+90+70=194

x	x-M=x-12	(x-12)2	x	(x-12)	(x-12)2	x	(x-12)	(x-12)2
14	2	4	5	-7	49	18	6	36
10	-2	4	7	-5	25	9	-3	9
17	5	25	12	0	0	15	3	9
13	1	1	8	-4	16	16	4	16
sum=54	6	sum=34	32	-16	sum=90	58	10	sim=70

within sum of square=SS_within=25+26+45=96

	x	x-M1=x-13.5	(x-13.5)2	x	x-M1=x-8	(x-8)2	x	x-M3=x-14.5	(x-14.5)2
	14	0.5	0.25	5	-3	9	18	3.5	12.25
	10	-3.5	12.25	7	-1	1	9	-5.5	30.25
	17	3.5	12.25	12	4	16	15	0.5	0.25
	13	-0.5	0.25	8	0	0	16	1.5	2.25
sum=	54	0	25	32	0	26	58	0	45
	M1=13.5			M2=8			M3=14.5

between Sum of square =SS_total-SS_within=194-96=98

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	98	2	49	4.59375	0.042181	4.256495
Within Groups	96	9	10.66667
Total	194	11

we reject the null hypothesis at 5% level of significance as the critical F=4.26 is less than calculated F=4.59(or p-value is less than alpha=0.05)