Question

3) An academic advisor at a university was studying student class attendance and would like to know if class attendance depends on school. a) State the Hypothesis to show class attendance depends on school. b) Choose a level of significance Use a = 0.05 for this problem. c) To test the hypothesis, the advisor obtained attendance records for 23 students (6 from engineering, 9 from business, and 8 from arts and sciences) for the fall term. The advisor determines the total number of lectures missed by each student. The data appear in the Absence worksheet in the HW4 data workbook on Moodle. d) Draw a conclusion and report that in the context of the problem. e) Use Fisher’s LSD Test with a= 0.05 to determine which schools’ students have significantly differently absence rates.

data:

Engineering	Business	Arts and Sciences
8	5	9
10	3	10
6	6	10
8	7	9
4	7	7
8	6	5
	2	13
	8	7
	1

Answer 1

a)

Ho:class attendance does not depends on school

H1:class attendance depends on school

b)

α=0.05

c)

One Way Analysis of Variance (ANOVA)              

	Engineering	Business	Arts and Sciences
count, ni =	6	9	8
mean , x̅ i =	7.333	5.000	8.750
std. dev., si =	2.066	2.449	2.435
sample variances, si^2 =	4.267	6.000	5.929
total sum	44	45	70		159	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				6.913043
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.176643562	3.65973535	3.37440926
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	1.059861374	32.9376181	26.9952741		60.99275
SS(within ) = SSW = Σ(n-1)s² =	21.33333333	48	41.5		110.8333

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   23
df within = N-k =   20
  
mean square between groups , MSB = SSB/k-1 =    30.49637681
  
mean square within groups , MSW = SSW/N-k =    5.541666667
  
F statistic = MSB/MSW =    5.50310559
P value =   0.012468464

anova table
	SS	df	MS	F	p-value	F-critical
Between:	60.993	2	30.496	5.503	0.0125	3.4928
Within:	110.833	20	5.542
Total:	171.826	22
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

d)

conclusion :    p-value<α , reject null hypothesis        

so, there is enough evidence to conclude that class attendance depends on school at α=0.05

e).

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	20
MSE	5.542
t-critical value,t(α/2,df)	2.086

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj))
if absolute difference of means > critical value,means are significnantly different ,otherwise not  

	Engineering	Business	Arts and Sciences
count, ni =	6	9	8
mean , x̅ i =	7.333	5.000	8.750

                   
                      

absolute mean difference		critical value			result
µ1-µ2	2.333	2.5881			means are not different
µ1-µ3	1.417	2.6520			means are not different
µ2-µ3	3.750	2.3861			means are different

so, business and art-science school students have significantly differently absence rates.