Question

A manufacturer of breakfast cereal is to release a new cereal called Smores. Before Smores is to be distributed in grocery stores across the country, the manufacturer conducts a study to determine if (i) the height of the shelf in which the cereal is to be displayed and (ii) the type of display will effect sales of the cereal.

A statistician was hired to design an experiment to investigate if - and if so, how - does the (i) shelf-height on which the cereal is to be displayed and (ii) how Smores will be advertised in-store influence sales. She randomly picked eighteen grocery stores in a certain geographical region, each store having a similar sized customer base. Two different `in-store' promotions were to be randomly assigned to eighteen stores.

For nine stores where Promotion A was used, three stores were asked to display Smores on the lower shelf, three on the middle shelf, and three on the upper shelf. The same was done for the nine stores where in store Promotion B was used. After a period of one week, the number of boxes of Smores sold at each of the 18 stores was recorded from the item-scanning system.

Use α=0.05 for any statistical tests.

	InStorePromtion	ShelfHeight	Sales
1	A	Bottom	47
2	A	Bottom	43
3	A	Bottom	44
4	A	Middle	64
5	A	Middle	65
6	A	Middle	68
7	A	Top	41
8	A	Top	43
9	A	Top	39
10	B	Bottom	46
11	B	Bottom	40
12	B	Bottom	42
13	B	Middle	67
14	B	Middle	71
15	B	Middle	70
16	B	Top	42
17	B	Top	43
18	B	Top	46

Complete the partial ANOVA table below, using two decimals in each field.

Source	Degrees of Freedom	Sum of Squares
Promotion Type
Shelf Height
Interaction
Error
Total

(b) You wish to test the hypothesis that the shelf-height will effect the sales of Smores. Of the options below, select the statistical hypothesis that will test this.
A. H0:μBottom=μMiddle=μTopHA:μBottom≠μMiddle≠μTopH0:μBottom=μMiddle=μTopHA:μBottom≠μMiddle≠μTop
B. H0:μBottom=μMiddle=μTopHA:atleastoneμiH0:μBottom=μMiddle=μTopHA:atleastoneμi isdifferentisdifferent
C. H0:μBottom≠μMiddle≠μTopHA:μBottom=μMiddle=μTopH0:μBottom≠μMiddle≠μTopHA:μBottom=μMiddle=μTop
D. H0:μPromoA=μPromoBHA:μPromoA≠μPromoBH0:μPromoA=μPromoBHA:μPromoA≠μPromoB


(c, i) Consider your statistical hypothesis in part (b). Compute the test statistic used to test H0H0 in part (b).

Fcalc=

(c, ii) Find the PP-value, using two decimals in your answer.

P-value=


(d) You wish to test the hypothesis that the type of Promotion will effect the sales of Smores. Of the options below, select the statistical hypothesis that will test this.
A. H0:μBottom=μMiddle=μTopHA:μBottom≠μMiddle≠μTopH0:μBottom=μMiddle=μTopHA:μBottom≠μMiddle≠μTop
B. H0:μBottom=μMiddle=μTopHA:atleastoneμiH0:μBottom=μMiddle=μTopHA:atleastoneμi isdifferentisdifferent
C. H0:X¯¯¯¯PromoA=X¯¯¯¯PromoBHA:X¯¯¯¯PromoA≠X¯¯¯¯PromoBH0:X¯PromoA=X¯PromoBHA:X¯PromoA≠X¯PromoB
D. H0:μBottom≠μMiddle≠μTopHA:μBottom=μMiddle=μTopH0:μBottom≠μMiddle≠μTopHA:μBottom=μMiddle=μTop
E. H0:μPromoA=μPromoBHA:μPromoA≠μPromoBH0:μPromoA=μPromoBHA:μPromoA≠μPromoB

(e, i) Consider your statistical hypothesis in part (d). Compute the test statistic used to test H0H0 in part (d).

Fcalc=

(e, ii) Find the PP-value, using FOUR decimals in your answer.


P-value =

(f) Is there an interaction between where the shelf-height at which the Smores are to be sold and the type of promotion used in the store? Find the test statistic and the PP-value for such a statistical test.

Fcalc=
P-value =

Answer 1