Question

A bake shop owner wants to know how to make his Bakalava (sweet walnut and honey pastry) to the maximum appeal for his patrons. He thinks that the major factors that determine appeal are the amounts honey in the filling and the number of layers of phillo dough used to make the pastry. During an eight week period he makes nine batches of Bakalva using a low, medium and high mount of honey and with 10, 15 and 20 layers of phillo dough. He then counts how many of each type he sells. The table below summarizes his sales of each variation on the basic (medium honey 15 layers) recipe.

Layers/ Honey	Low	Medium	High
10	100	105	105
15	98	100	123
20	118	122	59

Calculate a 2-factor χ² test to answer the following questions. Show enough of your work for part credit if you get the number wrong and use an α level of

0.05.

1. Is there a significant effect of recipe on sales?
2. Do honey and layers interact to produce a different appeal or are their ef-fects (if any) independent?
3. What do you think is the explanation for the results in terms of what ap-peals and does not appeal to the bake shop’s customers?

Answer 1

Observed
Layers/Honey	Low	Medium	High	Total
10	100	105	105	310
15	98	100	123	321
20	118	122	59	299
Total	316	327	287	930
Expected = Row Total* Column Total / Grand Total
Layers/Honey	Low	Medium	High
10	105.3333	109	95.66667
15	109.071	112.8677	99.06129
20	101.5957	105.1323	92.27204
Chi-square= Sum[(Exp-Obs)^2/Exp]
Layers/Honey	Low	Medium	High
10	0.270042	0.146789	0.910569
15	1.12373	1.467016	5.784922
20	2.648745	2.706312	11.99745
CHI_SQUARE = 27.0555713058413

Degrees of freedom = (#Rows – 1)(#Cols – 1) = 2*2 = 4
Critical value = X20.05;4 = 9.487729

Since Observed Chi-Square > critical value, we reject the null hypothesis of no association between the recipes and sales and conclude that there is significant association between recipes and sales.

Honey and layers interact significantly to produce a different appeal.