Question

Each of three supermarket chains in the Denver area claims to have the lowest overall prices. As part of an investigative study on supermarket advertising, a local television station conducted a study by randomly selecting nine grocery items. Then, on the same day, an intern was sent to each of the three stores to purchase the nine items. From the receipts, the following data were recorded. At the 0.025 significance level, is there a difference in the mean price for the nine items between the three supermarkets?

Item	Super's			Ralph's			Lowblaw's
1	$	1.29		$	4.36		$	3.10
2		1.37			1.87			1.87
3		1.21			2.40			1.72
4		2.01			4.15			2.22
5		1.57			2.10			2.40
6		1.35			5.05			4.21
7		2.46			3.75			3.90
8		1.25			3.10			4.21
9		2.40			4.15			1.80

1. State the null hypothesis and the alternate hypothesis.

For Treatment (Stores): Null hypothesis

1. H₀: μ₁ ≠ μ₂ ≠ μ₃

2. H₀: μ₁ = μ₂ = μ₃

• a

• b

2. Alternate hypothesis

• H₁: There is no difference in the store means.

• H₁: There is a difference in the store means.

3. For blocks (Items):

1. H₀: μ₁ = μ₂ = ... μ₉

2. H₀: μ₁ ≠ μ₂ ≠ ... μ₉

• a

• b

4. Alternate hypothesis

• H₁: There is no difference in the item means.

• H₁: There is a difference in the item means.

5. What is the decision rule for both? (Round your answers to 2 decimal places.)

Reject Ho if F>
For Stores=___
For Items=___

6. Complete an ANOVA table. (Round your SS, MS to 3 decimal places, and F to 2 decimal places.)

Source	SS	df	MS	F
Stores
Items
Error
Total

7. What is your decision regarding the null hypothesis? The decision for the F value (Stores) at 0.025 significance is:

• Reject H₀

• Do not reject H₀

8. The decision for the F value (Items) at 0.025 significance is:

• Reject H₀

• Do not reject H₀

9. Is there a difference in the item means and in the store means?

Answer 1

1)

H₀: μ₁ = μ₂ = μ_3
2)

H₁: There is a difference in the store means.

3)

H₀: μ₁ = μ₂ = ... μ₉

₄₎

H₁: There is a difference in the item means.
5)

Reject Ho if F>

for stores =4.69

for items =3.12

6)

Source of Variation	SS	df	MS	F
stores	14.724	2	7.362	11.45
items	10.518	8	1.315	2.05
Error	10.286	16	0.643
Total	35.529	26

7)

Reject H₀

8)

Do not reject H₀

₉₎

there  is a  in the store means

not in  item means