Question

1. A supermarket manager must decide how much of each ice cream flavor he should stock so that customer demands are satisfied and unwanted flavours don’t result in waste.  The ice cream supplier claims that among the four most popular flavours, customers have these preference rates: 62% prefer vanilla, 18% prefer chocolate, 12% prefer Neapolitan, and 8% prefer vanilla fudge.  A random sample of 200 customers produces the results summarized in the table below.  At α = 0.05, test the claim that the supplier has correctly identified customer preferences.

Answer 1

Hypothesis:

H0: the supplier do not correctly identified customer preferences

Ha: the supplier has correctly identified customer preferences.

Test:

	Observed(O)	Proportion(P)	Expected(E = n*P)	(O_E)^2/E
	120	0.62	124	0.129032258
	40	0.18	36	0.444444444
	18	0.12	24	1.5
	22	0.08	16	2.25
Total	200	1	200	4.323476703
df	3
alpha	0.05		X^2 Stat	4.3235
			X^2 Critical	7.8147
			P value	0.2286

Decision:

X^2 stat < X^2 critical, Do not reject H0

P value > 0.05, Do not reject H0

Conclusion:

There is not enough evidence to claim that the supplier has correctly identified customer preferences.

Note : Use X^2 table for X^2 critical and P values