Question

A consumer organization wants to know whether there is a difference in the price of a particular toy at three different store types. The price of the toy was checked in a sample of five discount stores, five variety stores, and five department stores. The sample results and the excel output are shown below:

Discount	Variety	Dept.
12	15	19
13	17	17
14	14	16
12	18	20
15	17	19

Anova: Single Factor

SUMMARY

Groups	Count	Sum	Average	Variance
Discount	5	66	13.2	1.7
Variety	5	81	16.2	2.7
Dep	5	91	18.2	2.7

ANOVA

Source of Variation	SS	df	MS	f	P-Value
Between Groups	63.33333	2	31.66667
Within Groups	28.4	12	2.366667

A) To test whether there is any difference in the pricing, state the null and alternative hypothesis of the formal test.
B) At alpha = 0.05, what is your conclusion? How od you know?
C) Multiple Choice: In the above experimental design test, you found:
a) we have insufficient evidence to conclude that there are different prices at the different store types.
b) There is no difference in prices at the different store types.
c) At least one of the store types charges different prices from the others.
d) The overall average price is $15.87.
e) All of the above.

D) Utilizing Fishers LSD, state which (if any) of the store types are different?

Answer 1

(A)

H0: Null Hypothesis: 1 = 2 = 3

HA: Alternative Hypothesis: 1   2    3

(B)

From the given ANOVA Table:

F = MSB/MSW = 31.66667/2.366667 = 13.380281

Degrees of freedom of numerator = 2

Degrees of freedom of denominator = 12

= 0.05

From Table, critical value of F = 3.885294

Since the calculated value of F is grater than critical value of F, Reject H0.

(C) Correct option:

(c) At least one of the store types charges different prices from the others.

(D)

To calculate the Least Significant Difference (LSD):

Step 1: To find the t - criical value:

= 0.05

dfw = 12

From Table, critical value of t = 2.1788

Step 2:

From ANOVA Table:

MSW = 2.366667

            

Step 3:

1 - 2 = 13.2 - 16.2 = - 4.2

Step 4:

= 4.2 > LSD = 2.1199

So,

we reject the Null Hypothesis that the means are the same and conclude that means of Discount Stores and Variety Stores are different.