Question

Question text

A researcher is interested in whether the attractiveness of the instructor influences student attendance at the statistics lab. The independent variable is the attractiveness of the lab instructor (assuming three instructors are of the same gender and are equally competent). The dependent variable is the number of times a student attends statistics lab during one semester. There are three groups with data:
Group 1(unattractive instructor): 20, 13, 9, 22, 21
Group 2: moderately attractive instructor: 24, 27, 25, 20, 29
Group 3: attractive instructor: 30, 24, 26, 28, 27
Based on the above information, 1) what is MSbetween? 2) what is the calculated F?, and 3) which group means are significantly different from each other based on Bonferroni correction?
Group 1 – Group 2: Significant Non-significant
Group 1 – Group 3: Significant Non-significant
Group 2 – Group 3: Significant Non-significant

Answer 1

	A	B	C
count, ni =	5	5	5
mean , x̅ i =	17.000	25.00	27.00
std. dev., si =	5.701	3.391	2.236
sample variances, si^2 =	32.500	11.500	5.000
total sum	85	125	135		345	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	23.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	36.000	4.000	16.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	180.000	20.000	80.000		280
SS(within ) = SSW = Σ(n-1)s² =	130.000	46.000	20.000		196.0000

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 =    140.0000
  
mean square within groups , MSW = SSW/N-k =    16.3333
  
F-stat = MSB/MSW =    8.5714

anova table	MS
	SS	df	MS	F	p-value	F-critical
Between:	280.00	2	140.00	8.57	0.0049	3.89
Within:	196.00	12	16.33
Total:	476.00	14
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

MSbetween = 140

F stat = 8.57

conclusion :    p-value<α , reject null hypothesis    

so means are different

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Level of significance	0.0166667
no. of treatments,k	3
DF error =N-k=	12
MSE	16.333
t-critical value,t(α/2,df)	2.779

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	-8.000	7.1044	-15.104	-0.896	means are different
µ1-µ3	-10.000	7.1044	-17.104	-2.896	means are different
µ2-µ3	-2.000	7.1044	-9.104	5.104	means are not different

Group 1 – Group 2: Significant
Group 1 – Group 3: Significant
Group 2 – Group 3: Non-significant

/.............................

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