Question

The manager of a supermarket chain wants to determine if the location of the product - where it is to be displayed - has any effect on the sale of a pet toys. Three different aisle locations are to be considered: the front of the aisle, the middle of the aisle, or the rear-aisle. Twenty-one stores are randomly selected, with 7 stores randomly assigned to sell the pet toy at the front-aisle, the middle-aisle, and the rear-aisle.

Front Middle Rear

8.6 3.2 4.6 7.2 2.4 6.0 5.4 2.0 4.0 6.2 1.4 2.8 5.0 1.8 2.2 4.0 1.6 2.8 4.5 1.8 2.5

A boxplot of the data is provided as well as MINITAB output:

1. (a) Does this data indicate that the sales of the pet toy are the same at the three aisle locations? State the appropriate statistical hypotheses.

2. (b) To test the H0 in part (a), an ANOVA table was obtained in MINITAB:

        Source  DF     SS     MS      F      P
        Factor   2  51.59
        Error
        Total   20  80.82
   

   The P-value of test was found to be 0.000106.
   (i) Provide the value of the test statistic from which this P -value was found.

⃝c Jim Stallard 2019: Reproduction, in whole or in part, requires written consent of the copyright holder.6

(ii) Using a level of significance of 5%, what can you conclude from this data? Write a brief sentence describing your finding. [2]

(c) The output below results from an application of Tukey’s HSD method.

   Front subtracted from:

            Lower  Center   Upper   --+---------+---------+---------+-------
   Middle  -5.553  -3.814  -2.076   (------*------)
   Rear    -4.024  -2.286  -0.547         (------*------)

                                    --+---------+---------+---------+-------
                                   -5.0      -2.5       0.0       2.5

   Middle subtracted from:

          Lower  Center  Upper   --+---------+---------+---------+-------
   Rear  -0.210   1.529  3.267                        (------*------)

Summarize these results.

Answer 1

(ii) Since p-value<0.05 so we reject H₀ at 5% level of significance and conclude that there is sufficient evidence that this data indicate that the sales of the pet toy are not same at the three aisle locations.

(c) Since the Confidence intervals of Middle-Front and Rear-Front do not contain zero hence Front is significantly different from Middle and Rear. Whereas Confidence interval of Rear-Middle contains zero hence they are not significantly different. Moreover we have seen that Confidence intervals of Middle-Front and Rear-Front do not contain only negative values hence we can conclude that average sale from front of the aisle is larger than other locations.