Question

In 2007, the United States experienced the biggest jump in food prices in 17 years (The Wallstreet Journal, April 1, 2008). A variety of reasons led to this result, including rising demand for meat and dairy products in emerging overseas markets, increased used of grains for alternative fuels, and bad weather in some parts of the world. A survey compared prices in $ of selected products at grocery stores in the Boston area. The dataset is available under: Files -> Dataset -> Mini-case 2 -> Mini2_Grocery In a report, use the sample information to: Determine whether differences exist in the average prices of products sold at the three stores at the 5% significance level Determine whether differences exist in the average prices of the 11 products at the 5% significance level Determine which stores’ prices differ using Fisher’s Least Significant Difference Method, if it is found that differences exist in the average prices among these stores. Use a 5% significance level.

Item	Crosby’s	Shaw’s	Market Basket
Two-liter Coke	1.89	1.59	1.50
Doritos Chips	4.29	4.99	3.80
Cheerios cereal	3.69	3.99	3.00
Prince spaghetti	0.89	1.69	1.19
Skippy peanut butter	5.49	4.49	3.99
Cracker Barrel cheese	4.99	5.99	4.49
Pepperidge Farm white bread	3.99	5.99	3.99
Oreo cookies	4.69	3.39	3.00
One dozen eggs*	1.49	2.49	1.59
Coffee*	4.49	4.79	3.99
Gallon of milk*	3.99	3.19	3.49

Answer 1

Determine whether differences exist in the average prices of products sold at the three stores at the 5% significance level

The hypothesis being tested is:

H₀: There is no difference in the average prices of products sold at the three stores

H_a: There is a difference in the average prices of products sold at the three stores

	Mean	n	Std. Dev
	3.626	11	1.5161	Crosby’s
	3.872	11	1.5504	Shaw’s
	3.094	11	1.1601	Market Basket
	3.531	33	1.4138	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	3.4819	2	1.74096	0.86	.4319
Error	60.4801	30	2.01600
Total	63.9620	32

The p-value is 0.4319.

Since the p-value (0.4319) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a difference in the average prices of products sold at the three stores.

Determine whether differences exist in the average prices of the 11 products at the 5% significance level

The hypothesis being tested is:

H₀: There is no difference in the average prices of the 11 products

H_a: There is a difference in the average prices of the 11 products

	Mean	n	Std. Dev
	1.660	3	0.2042	Two-liter Coke
	4.360	3	0.5981	Doritos Chips
	3.560	3	0.5076	Cheerios cereal
	1.257	3	0.4041	Prince spaghetti
	4.657	3	0.7638	Skippy peanut butter
	5.157	3	0.7638	Cracker Barrel cheese
	4.657	3	1.1547	Pepperidge Farm white bread
	3.693	3	0.8849	Oreo cookies
	1.857	3	0.5508	One dozen eggs*
	4.423	3	0.4041	Coffee*
	3.557	3	0.4041	Gallon of milk*
	3.531	33	1.4138	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	54.4951	10	5.44951	12.66	5.69E-07
Error	9.4669	22	0.43032
Total	63.9620	32

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the average prices of the 11 products.

Determine which stores’ prices differ using Fisher’s Least Significant Difference Method, if it is found that differences exist in the average prices among these stores. Use a 5% significance level.

Using the Fisher LSD Method and 95% Confidence

Factor	N	Mean	Grouping
Cracker Barrel cheese	3	5.157	A
Pepperidge Farm white bread	3	4.657	A	B
Skippy peanut butter	3	4.657	A	B
Coffee*	3	4.423	A	B
Doritos Chips	3	4.360	A	B
Oreo cookies	3	3.693		B
Cheerios cereal	3	3.560		B
Gallon of milk*	3	3.557		B
One dozen eggs*	3	1.857			C
Two-liter Coke	3	1.660			C
Prince spaghetti	3	1.257			C

Means that do not share a letter are significantly different.