The manager of a supermarket chain wants to determine if thelocation of the product - where it is to be displayed - has anyeffect on the sale of a pet toys. Three different aisle locationsare to be considered: the front of the aisle, the middle of theaisle, or the rear-aisle. Twenty-one stores are randomly selected,with 7 stores randomly assigned to sell the pet toy at thefront-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 4.01.6 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 arethe same at the three aisle locations? State the appropriatestatistical hypotheses.

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

      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 concludefrom this data? Write a brief sentence describing your finding.[2]

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

  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.