Question

Extra Credit (5 pts.) 4. A psychologist is interested in the level of anxiety for adolescents, the middle aged, and seniors. She recruits three samples and gives them a test that measures anxiety, with 1 being low anxiety and 10 being high anxiety. The group data are as follows: Adolescents M1 = 1 n = 5 T =5 SS, = 12 Middle Aged M2 = 5 n = 5 T2 = 25 Seniors M3 = 6 n = 5 T3 = 30 SS3 = 14 EX2 = 356 G = 60 N = 15 SS2 = 20 k = 3 Conduct the appropriate hypothesis test to determine if there is any difference (non- directional) in anxiety between groups at alpha=.05.

Answer 1

	A	B	C
count, ni =	5	5	5
mean , x̅ i =	1.000	5.00	6.00
std. dev., si =	1.732	2.236	1.871
sample variances, si^2 =	3.000	5.000	3.500
total sum	5	25	30		60	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	4.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	9.000	1.000	4.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	45.000	5.000	20.000		70
SS(within ) = SSW = Σ(n-1)s² =	12.000	20.000	14.000		46.0000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    35.0000
  
mean square within groups , MSW = SSW/N-k =    3.8333
  
F-stat = MSB/MSW =    9.1304

anova table
	SS	df	MS	F	p-value	F-critical
Between:	70.00	2	35.00	9.13	0.0039	3.89
Within:	46.00	12	3.83
Total:	116.00	14

       α =    0.05
conclusion :    p-value<α , reject null hypothesis        
so, means are not equal

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