A national distributor of \"Eagle\" brand snacks is attempting to develop a mode

Question

A national distributor of "Eagle" brand snacks is attempting to develop a model to explain sales of their product. To do so, data have been gathered on monthly sales (measured in hundreds of dollars) from its many marketing areas. From these, sixty observations have been selected at random.

The variables in the data set are in columns, one observation per line (row). The first column is variable number 1, the second is variable number 2, etc. You must download your data set from the link on our class web page.

Your downloaded data set will contain only the data records without header lines.

The data reported in the data set are as follows:

     Variable #1 = Monthly sales in thousands of dollars per marketing area.

This is the variable in which the company is primarily interested. They would like to determine what factors have an effect on their sales. They would also like to be able to predict sales based upon these factors, once they are identified. This variable will be the dependent variable in your analyses.

The company has also identified several potential explanatory factors that may have an effect on Eagle Chip sales. These are identified below and available in your data set. Variables 2 through 6 are quantitative high-level measurements. Variable 7 is qualitative having four nominal levels identified below.

   Variable #2 = Promotional budget for the sales area, in thousands of dollars.
                    3 = Median family income in the sales area, in thousands of dollars.
                    4 = Product recognition index, proportion of respondents to a marketing survey in the market
district that recognized the Eagle brand name (reported as a decimal value).
                    5 = Average retail price of product in dollars.
                    6 = Average retail price of leading competitor brand in dollars.
                    7 = A coded variable representing the advertising method employed in the sales area.
                        There are four levels of this categorical variable labeled A, B, C, and D as follows:
                            A = Sports Magazine only
                            B = Radio Sport Show Ads
                            C = TV Sports Show Ad
                            D = TV General Advertising

Download your data set, import your data set into Excel, label your variables, and save your Excel file. You will use this Excel file for the next three computer projects.
ANOVA Project

The company is primarily interested in developing a model to explain and predict sales. Company sales (variable number 1) will be your dependent variable in these analyses.

Part A.

Provide summary descriptive statistics for company sales.

Part B.

The company is interested in determining which, if any, of the advertising methods used might lead to the highest average sales level and has asked you to do the analysis to provide this information. It will be possible to make this determination since each observation in the sample was generated using only one of the four advertising methods.

Perform an analysis of variance on Excel as demonstrated in class using Sales (variable number 1) as the dependent variable and Advertising Method (variable 7) as the explanatory variable.

Present your ANOVA results from your Excel printout using a “cut and paste” or screen capture method and respond to the following:

Specify the null and alternative hypotheses for the F-test for this model.

Report the critical value of the test statistic -or- interpret the p-level for this test.

State your conclusion regarding the test result.

Interpret your finding; in particular, make certain that you respond to the company’s inquiry.

A B C D 75 61.4 140 123.2 51.5 79.7 131.9 119.8 70.3 81.2 96.3 80 73.8 94.1 96.5 111.1 46.6 85.8 90.1 76 61.4 90.5 112.3 101.4 83.4 80.5 119.2 97.8 60.7 96.5 110.7 108.2 98.2 87.4 96.2 86.5 93.7 86 99.3 69.5 85.3 92.6 115.7 94.5 79.7 99.9 113.6 71.1 72.5 112.7 60 101.7 106.3 84.5 100.2 86.4 80.4 108.5 124.4 77

Explanation / Answer

Part A.

Provide summary descriptive statistics for company sales.

Solution:

Descriptive statistics for the company sales is summarised as below:

Monthly Sale in $'000

Mean

91.51166667

Standard Error

2.543939393

Median

91.55

Mode

61.4

Standard Deviation

19.70526981

Sample Variance

388.2976582

Kurtosis

-0.124099752

Skewness

0.078110782

Range

93.4

Minimum

46.6

Maximum

140

Sum

5490.7

Count

60

Part B.

Solution:

Here we have to check the hypothesis or claim whether the average monthly sales for four different advertising methods is same or not. For checking this claim, we have to use the one way analysis of variance or single factor ANOVA. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any statistically significant difference between average monthly sales for four different methods.

Alternative hypothesis: Ha: There is a statistically significant difference between average monthly sales for four different methods.

In symbolic form, null and alternative hypotheses are given as below:

H0: µa = µb = µc = µd V/s Ha: µa µb µc µd or at least one pair is not equal.

The ANOVA table for this test is given as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

A

14

1010.7

72.19286

229.873

B

18

1566.2

87.01111

125.4716

C

17

1845.8

108.5765

234.5282

D

11

1068

97.09091

315.3189

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

10882.56

3

3627.518

16.89041

6.2E-08

2.769431

Within Groups

12027.01

56

214.768

Total

22909.56

59

For this ANOVA test, the test statistic value F is given as 16.89 with the p-value as 0.00.

(Please note, P-value 6.2E-08 = 0.000000062 approximately equal to 0.00.)

We assume 5% level of significance or alpha = = 0.05.

For this test, P-value < , so we reject the null hypothesis.

We reject the null hypothesis that there is no any statistically significant difference between average monthly sales for four different methods.

There is sufficient evidence to conclude that there is a statistically significant difference between average monthly sales for four different methods.

Monthly Sale in $'000

Mean

91.51166667

Standard Error

2.543939393

Median

91.55

Mode

61.4

Standard Deviation

19.70526981

Sample Variance

388.2976582

Kurtosis

-0.124099752

Skewness

0.078110782

Range

93.4

Minimum

46.6

Maximum

140

Sum

5490.7

Count

60

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