Question

14) (20) Does the presence of others affect people's willingness to assume responsibility for the welfare of others? For example, does the presence of other people affect our reaction to potentially dangerous smoke seeping from a wall vent? To answer this question, a researcher measured how long (in seconds) it took subjects to ask for help as smoke gradually filled a waiting room. The room was occupied by a subject plus "crowds" of either zero, two, or four experimental confederates (confederates are research assistants who pretend they are subjects) who acted as if they were regular subjects but ignored the smoke. Here are some summary data: zero confederates T = 15 n = 3 SS = 14 two confederates T = 39 n=3 SS = 14 four confederates T = 54 n = 3 SS = 8

Answer 1

a)

treatment	G1	G2	G3	G4	G5
count, ni =	3	3	3
mean , x̅ i =	5.000	13.00	18.00
std. dev., si =	2.6	2.6	2.0
sample variances, si^2 =	7.000	7.000	4.000
total sum	15	39	54				108	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	12.00
( x̅ - x̅̅ )²	49.000	1.000	36.000
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	147.000	3.000	108.000				258
SS(within ) = SSW = Σ(n-1)s² =	14.000	14.000	8.000				36.0000

no. of treatment , k =   3  
df between = k-1 =    2  
N = Σn =   9  
df within = N-k =   6  
      
mean square between groups , MSB = SSB/k-1 =    258/2=   129.0000
mean square within groups , MSW = SSW/N-k =    36/6=   6.0000
      
F-stat = MSB/MSW =    129/6=   21.5000

anova table
	SS	df	MS	F	p-value	F-critical
Between:	258.00	2.00	129.00	21.50	0.002	5.143
Within:	36.00	6.00	6.00
Total:	294.00	8.00
					α =	0.05

F stat > citical value , reject Ho

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Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	6
MSE =	6.0000
q-critical value(0.05,3,6)=	614

critical value = q*√(MSE/2*(1/ni+1/nj))  

=8.68

					confidence interval
	mean difference	absolute mean difference		critical value	lower limit	upper limit			result
µ1-µ2	-8.00	8.00		8.68	-16.68	0.68			no, means are not different
µ1-µ3	-13.00	13.00		8.68	-21.68	-4.32			yes, means are different
µ2-µ3	-5.00	5.00		8.68	-13.68	3.68			no, means are not different

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