blackboard·ohio.edu 0.14 0.33 4 Santa Rosa Torrance 1 of 1 Three Wal-Mart stores

ID: 3317287 • Letter: B

Question

blackboard·ohio.edu 0.14 0.33 4 Santa Rosa Torrance 1 of 1 Three Wal-Mart stores in Texas have been in business for 35 years. Annual sales at each of the three stores over that time period have a normal distribution, and variances of the three sets of sales data are approximately equal Six of the 35 years of data were randomly chosen for this problem. Consider the observations as independent and the six years of sample data as parametric. Determine whether or not these three stores differed significantly in sales amounts for the sampled years. Use the 0.05 level of significance. The following data represent millions of dollars of sales per year Lake Store 15.3 16.1 13.0 13.7 12.2 10.5 Davis Store 13.4 17.7 15.9 16.8 17.9 16.2 Kearn Store 11.3 14.8 14.7 13.9 16.5 14.3 From the randomly sampled data listed below, which has independently been shown to be parametric, determine

Explanation / Answer

Solution:

Here, we have to use one way analysis of variance or ANOVA F test for checking the significant difference in sales amounts for the sampled years. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any statistically significant difference exists between the average sales amounts for given three stores.

Alternative hypothesis: Ha: There is a statistically significant difference exists between the average sales amounts for given three stores.

We are given level of significance = = 0.05

For the given data, the mean and standard deviations are given as below:

No.

Lake Store

Davis Store

Kearn Store

15.3

13.4

11.3

16.1

17.7

14.8

15.9

14.7

13.7

16.8

13.9

12.2

17.9

16.5

10.5

16.2

14.3

Total

80.8

97.9

85.5

Mean

13.47

16.32

14.25

2.05

1.63

1.70

From the given data, we have

N1 = 6, df1 = 5

N2 = 6, df2 = 5

N3 = 6, df3 = 5

X1bar = 13.47

X2bar = 16.32

X3bar = 14.25

Grand Mean = GM = (X1bar + X2bar + X3bar) / 3 = (13.47 + 16.32 + 14.25) / 3 = 14.68

Total number of groups = k = 3

Between degrees of freedom = k – 1 = 2

Total sample size = N = 6 + 6 + 6 = 18

Total degrees of freedom = N – 1 = 18 – 1 = 17

Within degrees of freedom = Total degrees of freedom – between degrees of freedom

Within degrees of freedom = 17 – 2 = 15

Variance of means = ((X1bar – GM)^2 + (X2bar – GM)^2 + (X3bar – GM)^2)/ between df

Variance of means =( (13.47 – 14.68)^2 + (16.32 – 14.68)^2 + (14.25 – 14.68)^2 / 2)

Variance of means = 2.1693

SS between = Variance of means*N1 = 2.1693*6 = 13.0158

SS within = (S1^2 + S2^2 + S3^3) / k = (4.2025 + 2.6569 + 2.89) / 3 = 3.2498

MS between = 13.0158/2 = 6.5079

MS within = 3.2498/15 = 0.216653333

F = MS between / MS within = 6.5079/0.216653333 = 30.0383101

P-value = 0.00

= 0.05

P-value < = 0.05

So, we reject the null hypothesis that there is no any statistically significant difference exists between the average sales amounts for given three stores.

There is sufficient evidence to conclude that there is a statistically significant difference exists between the average sales amounts for given three stores.

No.