Question

There are four McWendy King restaurants in the city of Burgerville; one in the metropolitan area, one at the market plaza, one at Burger University, and one at the river. To compare the mean sales of burgers at the four restaurants, six weeks were randomly selected, and the number of burgers sold were recorded. Assume that weekly sales of burgers at the four restaurants are normally

at each restaurant distributed.

RESTAURANT :

Metro; Market plaza; University; River

Week 1 130 160 320 190

Week 2 230 220 340 230

Week 3 428 290 290 240

Week 4 111 245 310 170

Week5 243 205 280 180

Week 6 310 260 260 190

a) Define (1) the response variable, (2) the treatment factor, (3) and the block factor.

b) At α = 0.10, is there sufficient evidence to suggest a difference in the mean numbe

of burgers sold at the different restaurants? Comment on the validity of the result.
c) Is week a useful blocking factor in this investigation? Test using a 10% level of significance.

d) If you rejected the null hypothesis in (b), construct simultaneous 90% Tukey confidence intervals to

discuss the nature of the differences in mean sales of burgers at the different restaurants.

e) Use a nonparametric procedure to determine if, on average, there is a difference in the number of burgers

sold at the different restaurants at a 10% level of significance.

Answer 1

a)

response variable is sales of burger

treatment factor is four restaurant

block factor is 6 weeks

b)

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
week1	4	800	200	7000
week2	4	1020	255	3233.333
week3	4	1248	312	6536
week4	4	836	209	7540.667
week5	4	908	227	1919.333
week6	4	1020	255	2433.333
metro	6	1452	242	13814
market	6	1380	230	2070
univst	6	1800	300	840
rivar	6	1200	200	800
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	33240	5	6648	1.833762	0.166611	2.27302245
Columns	31608	3	10536	2.906216	0.069163	2.48978773
Error	54380	15	3625.333
Total	119228	23

p value for sales of different restaurant = 0.069

p value < 0.1, so result is significant

so, there sufficient evidence to suggest a difference in the mean number of burgers sold at the different restaurants

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

c)

p value for block factor = 0.166611  

p value > 0.1, so not significant

so, week is not a useful blocking factor in this investigation

..........

d)

Level of significance	0.1
no. of treatments,k	4
DF error =N-k=	15
MSE	3625.333
q-statistic value(α,k,N-k)	3.5400

critical value = q*√(MSE/n)      

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	12.00	87.02	-75.02	99.02	means are not different
µ1-µ3	-58.00	87.02	-145.02	29.02	means are not different
µ1-µ4	42.00	87.02	-45.02	129.02	means are not different
µ2-µ3	-70.00	87.02	-157.02	17.02	means are not different
µ2-µ4	30.00	87.02	-57.02	117.02	means are not different
µ3-µ4	100.00	87.02	12.98	187.02	means are different

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

thanks

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