Question

The following data represents the number of packages of 5 popular brands of cigarettes sold by a supermarket on 8 randomly selected days:

 

Brand

A

B

C

D

E

21

35

32

28

14

47

25

38

35

12

27

41

19

23

31

20

45

60

33

36

31

40

43

48

32

53

29

42

40

23

35

42

45

29

31

22

36

29

42

30

 

 

Perform an analysis of variance, at 0.05 level of significance, and determine whether or not the 5 brands sell, on the average, the same number of cigarettes at this supermarket. (15 points)

 

 

Answer 1

One Way ANOVA

$H_0: \mu_1=\mu_2=\mu_3=\mu_4=\mu_5$ , 5 brands sell, on the average, the same number of cigarettes at the supermarket

$H_a: not\ (\mu_1=\mu_2=\mu_3=\mu_4=\mu_5)$ , 5 brands sell, on the average, not the same number of cigarettes at the supermarket

F statistic:

F = MSG / MSE = 2.725

where:

Mean Square between groups:

MSG = SSG / (k - 1) =237.24

k = 5 is number of groups

Sum of Squares between groups:

$SSG=\sum n_i (\overline{x}_i-\overline{x})^2=948.98$

Mean Square within groups:

MSE = SSE / (n - k) = 87.05

n = 45 overall sample size

Sum of Squares within groups:

$SSE=\sum (n_i-1)s^2_i=3482$

Degrees of Freedom:

between groups: $k-1=4$

within groups: $n-k=40$

critical value:

$F{crit}=2.606$

Since $F>F{crit}$ we reject null hypothesis. 5 brands sell, on the average, not the same number of cigarettes at the supermarket.