Question

Forty-eight participants were randomly assigned to do math tasks under one of three conditions: 16 while listening to soft gentle music, 16 while listening to loud intense music, and 16 while in silence. The means and estimated population variances for the three groups were: Soft-gentle: M = 33, S² = 25; Loud-intense: M = 42, S² = 36; Silence M = 42, S² = 16.
Do these results suggest that there is a difference in performance on this kind of math task under these three conditions? (Use the .05 level.)

Choose the appropriate test and use the five steps of hypothesis testing.      

Answer 1

	A	B	C
count, ni =	16	16	16
mean , x̅ i =	33.000	42.00	42.00
std. dev., si =	25.000	36.000	16.000
sample variances, si^2 =	625.000	1296.000	256.000
total sum	528	672	672		1872	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	39.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	36.000	9.000	9.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	576.000	144.000	144.000		864
SS(within ) = SSW = Σ(n-1)s² =	9375.000	19440.000	3840.000		32655.00

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   48
df within = N-k =   45
  
mean square between groups , MSB = SSB/k-1 =    432.0000
  
mean square within groups , MSW = SSW/N-k =    725.6667
  
F-stat = MSB/MSW =    0.5953

anova table
	SS	df	MS	F	p-value	F-critical
Between:	864.00	2	432.00	0.60	0.5557	3.20
Within:	32655.00	45	725.67
Total:	33519.00	47

       α =    0.05
conclusion :    p-value>α , do not reject null hypothesis        
          
there is NOT a difference in performance on this kind of math task under these three conditions

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