Question

A company is trying to choose between three types of cars for its fleet: national, Japanese or European. Five cars of each type are ordered and after traveling 10,000 miles with them, the cost per mile traveled (cents) of each car is calculated.

Nationals: 18.0, 17.6, 17.4, 19.1, 16.9

Japanese: 15.1, 16.6, 16.1, 15.3, 15.4

Europeans: 19.3, 17.4, 17.1, 18.6, 16.1

1) Make the hypothesis test (6 steps). In step 1, Ho and H1, write them in a text (don't write Ho:

2) Take the Tukey test. What type of car do you recommend?

Answer 1

	A	B	C	D
count, ni =	5	5	5
mean , x̅ i =	17.800	15.70	17.70
std. dev., si =	0.828	0.628	1.263
sample variances, si^2 =	0.685	0.395	1.595
total sum	89	78.5	88.5		256	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	17.07
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.538	1.868	0.401
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	2.689	9.339	2.006		14.03333
SS(within ) = SSW = Σ(n-1)s² =	2.740	1.580	6.380		10.7000

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 =    7.0167
  
mean square within groups , MSW = SSW/N-k =    0.8917
  
F-stat = MSB/MSW =    7.8692

anova table
	SS	df	MS	F	p-value	F-critical
Between:	14.03	2	7.02	7.87	0.0066	3.89
Within:	10.70	12	0.89
Total:	24.73	14
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

................

TUKEY:

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	12
MSE	0.892
q-statistic value(α,k,N-k)	3.7700

critical value = q*√(MSE/n)

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	2.10	1.59	0.51	3.69	means are different
µ1-µ3	0.10	1.59	-1.49	1.69	means are not different
µ2-µ3	-2.00	1.59	-3.59	-0.41	means are different

...............

JAPANESE CAR IS RECOMMENDED

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THANKS

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