Question

A firm wanted to test for alternative types of packaging (A, B, C & D) for one of its products. Specifically, it wanted to determine whether there was any significant difference in consumer preference between the four types of packaging. It conducted a consumer preference test in which a sample of 200 consumers participated. Each participant was shown the four types and asked to pick the one they preferred the most. The results of these tests where as follows: Of the 200 consumers, 40 preferred A, 55 preferred B, 60 preferred C, and 45 preferred D. From these results, can one conclude a 95% confidence that there is some significant difference in preference across the four types of packaging?

Answer 1

null hypothesis: Ho:all  four types of packaging have similar preference

alternate hypothesis: Ha: there is significant difference in preference across the four types of packaging

degree of freedom =categories-1=4-1=3

for 3 degree of freedom and 0.05 level rejection region >7.815

applying chi square goodness of fit:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
A	0.250	40.000	50.000		2.000
B	0.250	55.000	50.000		0.500
C	0.250	60.000	50.000		2.000
D	0.250	45.000	50.000		0.500
total	1.000	200	200		5.000

as test statsitic 5.00 is not in rejection region we can not reject null hypothesis

we do not have evidence to coclude at 0.05 level that there is significant difference in preference across the four types of packaging