Retail Prices Of Flu And Cold Drugs

Retail Prices of Flu and Cold Drugs:

Data:

This is a report that compared product prices in a number of stores, pharmaceutical products prices sold at Wal-Mart, Target, Kmart and CVS were selected, the following is a list of products selected:

flu and cold products

Wal-Mart

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Retail Prices of Flu and Cold Drugs

CVS

Target

Kmart

Mucinex

$11.37

$13.12

$11.44

$12.99

Tylenol

$11.66

$11.83

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Retail Prices of Flu and Cold Drugs

$11.78

$11.50

Ricoal green tea

$5.01

$4.67

$5.22

$5.66

Puraline

$5.88

$6.39

$6.22

3/24

Retail Prices of Flu and Cold Drugs

$5.99

Cepacol

$3.96

$3.44

$3.07

$2.99

total

$37.88

$39.45

$37.73

$39.13

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Retail Prices of Flu and Cold Drugs

mean

$7.58

$7.89

$7.55

$7.83

The main objective is to determine whether the prices in the stores are different, the construction of the ANOVA table will involve determining the difference within and between the groups, the first step is to square the prices and determining the sum of these squares as follows:

Wal-Mart

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Retail Prices of Flu and Cold Drugs

w2

cvs

c2

target

t2

Kmart

k2

grand total

Mucinex

11.37

129.3

13.12

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Retail Prices of Flu and Cold Drugs

172.1344

11.44

130.8736

12.99

168.7

Tylenol

11.66

136

11.83

139.9489

7/24

Retail Prices of Flu and Cold Drugs

11.78

138.7684

11.5

132.3

Ricoal green tea

5.01

25.1

4.67

21.8089

5.22

27.2484

8/24

Retail Prices of Flu and Cold Drugs

5.66

32.04

Puraline

5.88

34.57

6.39

40.8321

6.22

38.6884

5.99

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Retail Prices of Flu and Cold Drugs

35.88

Cepacol

3.96

15.68

3.44

11.8336

3.07

9.4249

2.99

8.94

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Retail Prices of Flu and Cold Drugs

total

11/24

Retail Prices of Flu and Cold Drugs

37.88

39.45

37.73

39.13

154.19

mean

7.576

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Retail Prices of Flu and Cold Drugs

7.89

7.546

7.826

13/24

Retail Prices of Flu and Cold Drugs

sum of squared price

340.6

386.5579

14/24

Retail Prices of Flu and Cold Drugs

345.0037

377.8

1449.996

n

5

5

5

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Retail Prices of Flu and Cold Drugs

5

20

sum of squared prices / n

68.12

77.31158

69.00074

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Retail Prices of Flu and Cold Drugs

75.57

289.9992

Using the above results the values of I, II and III are determined as follows:

I

(price grand total)                                                 2

(154.19*154.19)/20 = 1189

II

total sum of squared  prices for all groups

/  total n

1449.996

III

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Retail Prices of Flu and Cold Drugs

Grand total( sum of  squared price/ n)

289.9992

Using the values above the ANOVA table is stated as follows:

variation source

SS

df

ms

between

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Retail Prices of Flu and Cold Drugs

III-I

k-1

III-I/k-1

within

II-III

N-k

II-III/n-k

total

II-I

n-1

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Retail Prices of Flu and Cold Drugs

And the F statistics value will be determined as follows:

F = [(III-I)/ (k-1)]/ [(II-III)/ (n-k)]

The following are the results:

variation source

SS

df

ms

f

between

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Retail Prices of Flu and Cold Drugs

-898.728585

3

-299.6

-4.1321

within

1159.99688

16

72.5

total

261.268295

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Retail Prices of Flu and Cold Drugs

19

Hypothesis:

H0: W=C=T=K

H1: W≠C≠T≠K

Where W is Wal-Mart mean price, C is CVS mean price, T is Target mean price and K Kmart mean price.

The F statistics value = -4.1321

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Retail Prices of Flu and Cold Drugs

The selected F test level is α= 0.01

From the F table the critical value = 2.3970

The F critical value > F statistics value calculated

Results:

The above results show that F critical > F statistics, meaning that the null hypothesis W=C=T=K is accepted, we conclude that the mean prices across the four retailers are equal at the 0.01 f test level.

Conclusion:

At the 0.01 level of test the null hypothesis that all the prices are equal across all the four retailers, this means that the prices for the selected products are relatively equal and there exist no significant differences in prices.

References:

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Retail Prices of Flu and Cold Drugs

Cummings, J. and Bailey, W. (2002) Statistics, McGraw Hill Press, New  York

December, from http://www.cvs.com/CVSApp/catalog/shop_category.jsp?filterBy=&navA ction=push&navCount=1&itemId=cat15

Kmart (2009) Pharmacy: product prices, retrieved on 10th December, from www.kmart.com/pharmacy

December, from http://www.target.com/b/ref=in_br_browse-box/181-5908270-7641256?ie=UT F8&node=1233225011

December, from http://www.walmart.com/browse/Medicine-Cabinet/Cough-Cold-Flu/_/N-8z5u Zaq90Zaqce/Ne-8z31?ic=48_0&ref=418717.418818&tab_value=11790_All&cat NavId=976798

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