This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.

 

ABSTRACT

The goal of this study was to determine if Wal-Mart has significantly lower original (non-sale) prices than Kroger’s original prices. Based on the general consensus that Wal-Mart has lower prices, the expected outcome was that Wal-Mart does in fact have lower prices. A one sample t-test, with alpha level .05, was used to determine if there is no difference between Kroger and Wal-Mart’s prices, or if there is a difference in the prices which indicates that Wal-Mart has lower prices.

METHODOLOGY

            This study wanted to compare the prices of various items at Wal-Mart and Kroger to prove Wal-Mart offers consistently lower prices.

            First, a list of sixty products sold at both Wal-Mart and Kroger, numbered 1-60, was created  The random number generator function on a graphing calculator was used to randomly select 40 of those 60 products to be compared.  True randomization was not possible, due to the fact that we could not obtain complete product lists for all items sold at both Kroger and Wal-Mart.

            To minimize variability, prices at both stores were compared on the same day, May 12th, 2008. The original price of each item selected was recorded. If the item was on sale, the non-sale price of the item was taken. After both stores were visited, the difference between the prices (Kroger – Wal-Mart) was calculated.

            After the difference between the Wal-Mart and Kroger prices was computed, the

 

 sample mean () and standard deviation (Sx) were found.

 

 

= ∑ (Kroger Price-Wal-Mart Prices) / Number of Items

= $20.68 / 40

= .52

Sx=  s / √ n

Sx= .4944 / √ 40

Sx= .07817

 

Explanatory Data Analysis

Assumptions:

SRS

Normally Distributed     

n= 40, therefore it is appropriate to use a normal approximation because of the Central Limit Theorem.

 

α = .05 

df= 39

 

µ = Mean difference between Kroger and Wal-Mart prices

H0 : µ = 0

Ha : µ > 0

 

t-test statistic:

 t = ( - µ) / Sx

 t = .52-0 / .07871

 t = 6.652

 

Probability (t > 6.652, df=39) = 3.23 x 10 -8

 

 

Because our data gives a p-value of 3.23 x 10 -8 df=39, our data is statistically significant at the α = .05 level therefore we can reject H0 in favor of Ha.  Meaning we can reject the hypothesis that there is no difference in the mean prices at Wal-Mart and Kroger in favor of the hypothesis which states that Wal-Mart has lower prices.

As previously stated, it was not possible to obtain true randomization because a list of all items sold at both Kroger and Wal-Mart was not available. Therefore, we generated a population from which we drew our random sample. Prices for the items were retrieved from one Wal-Mart and one Kroger, both located in Lexington, Ky. If many Kroger and Wal-Mart stores were visited we believe the result would not be significantly different because of the p-value our data yielded was much smaller than the alpha level .05.

 

 

Random Sample

Kroger Price

Wal-Mart Price

Difference

1.       Pepperidge Farm sliced bread

$2.79

$2.68

$0.11

2.       Honey Maid Graham crackers

$3.47

$4.18

-$0.71

3.       Barilla Angel hair pasta

$1.35

$1.28

$0.07

4.       Star Kist Tuna

$1.49

$0.68

$0.81

5.       Ramen noodles

$0.18

$0.14

$0.04

6.       Regular Hersey’s bar

$0.59

$0.33

$0.26

7.       Chips Ahoy chocolate chip cookies

$3.79

$3.28

$0.51

8.       Lucky Charm’s cereal

$3.19

$2.52

$0.67

9.   Colgate total toothpaste

$3.64

$2.44

$1.20

10.   Oscar Meyer 8-pack hot dogs

$2.89

$1.50

$1.39

11.   Breyer’s Vanilla ice cream

$3.99

$3.50

$0.49

12.   Ocean spray Cranberry juice

$3.28

$2.88

$0.40

13.   Hidden Valley Ranch dressing

$3.49

$2.44

$1.05

14.   Velveeta cheese

$3.75

$3.48

$0.27

15.   Herbal Essence Shampoo

$3.15

$2.94

$0.21

16.   Snyder’s Pretzels

$2.39

$2.16

$0.23

17.   8 20 fl oz. Powerade

$5.69

$4.48

$1.21

18.  Dayquil

$4.99

$4.27

$0.72

19.   Dial soap

$1.88

$1.76

$0.12

20.   Traditional Prego sauce

$2.69

$2.16

$0.53

21.   Vlasic Dill Pickles

$3.39

$2.24

$1.15

22.   Hefty garbage bag

$7.99

$6.78

$1.21

23.   Smart one’s Mac and cheese

$2.86

$1.76

$1.10

24.   Planter’s peanuts

$3.59

$3.57

$0.02

25.   Chewy Chocolate chip granola bars

$2.20

$2.18

$0.02

26.   Purina cat chow

$4.69

$4.12

$0.57

27.   Smucker’s Strawberry Jelly

$3.99

$2.84

$1.15

28.   Lipton pasta sides

$1.65

$1.22

$0.43

29.   Philadelphia cream cheese

$1.94

$1.76

$0.18

30.   Jiff peanut butter

$4.39

$3.14

$1.25

31.   Cascade dish soap

$3.69

$3.50

$0.19

32.   Nesquik Chocolate milk

$3.99

$3.63

$0.36

33.   Women’s Venus razors

$8.74

$7.44

$1.30

34.   12-pack coke

$4.99

$3.78

$1.21

35.   Charmin Ultra soft four pack

$4.69

$4.26

$0.43

36.   Campbell’s chicken noodle soup

$0.73

$0.68

$0.05

37.   Oranges

$0.99

$0.64

$0.35

38.   Kraft Macaroni and Cheese (box)

$0.71

$0.78

-$0.07

39.   Tide laundry detergent (50 fl oz.)

$7.15

$6.97

$0.18

40.   Dole canned pairs

$1.34

$1.32

$0.02

Sum

$20.68

Average

$0.52

St. Deviation

0.4944

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                  

 

 

 

 

 

 

Kroger Prices v. Wal-Mart Prices