19 For a given completely randomized experiment related to involving sales volum

Question

19 For a given completely randomized experiment related to involving sales volume marketing media, EXCEL produced the following tables: SUMMARY STATISTICS Average Sales Volume Media Variance (Units) Count Sum 112.5 188 940 48.66667 Radio 680 170 124 Internet. 522 174 ANOVA. P-value F critical Source of Variation Sum of Degrees of Mean Squares freedom Square 2 400.5 4.270735 0.049636 4.256495 801 Between Treatments 93.77778 Within Treatments 844 1645 Total a. How many observations were recorded for this experiment? b. What, exactly, is the null hypothesis being tested? c. At a 0.05, what is the rejection decision and why? d. What is the test conclusion? e. Using the Tukey-Cramer procedure, which of the three media listed are statistically different (if any)? Show all work below.

Explanation / Answer

Part (a)

Number of observations recorded in the experiment is 12. The clue comes from Degrees of Freedom for ‘Total’ in the given ANOVA table. Degrees of Freedom for ‘Total’ is (total number of observations - 1). [One could also get this by adding the ‘count’ given for the three media.]

Part (b)

Null hypothesis is: The three different media yield the same sales volume.

Statistically, the model for CRD is: xij = µ + i + ij, where xij = jth observation on ith treatment, µ = common effect, i = effect of ith treatment (media in the current question) and ij is the error term. In terms of this model, Null hypothesis is H0: 1 = 2 = 3.

Part (c)

At = 0.05, Null hypothesis is rejected since F value > F-critical [vide ANOVA table]

Same inference can also be made by p-value since it is less than 0.05.

[cautionary note: as a class room example to illustrate the concept and working, it is perfectly fine to reject the hypothesis since the criteria are fulfilled. But practically, one needs to be very careful in such situations since the difference between F value and F-critical as also between the level of significance and p-value is very small, which could have as well arisen due to rounding off errors.]

Part (d)

The conclusion is that it is statistically reasonable to suggest that the three different media yield different sales volume.

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