Question

A dept. Store marketing study claims 40% of customers prefer Calvin Klein, 30% prefer Tommy Hilfiger, 20% prefer Ralph Lauren and 10% prefer other. A survey of 500 customers finds the following: 175 prefer Calvin Klein, 150 prefer Tommy Hilfiger, 150 Prefer Ralph Lauren and 25 prefer other.

Test the goodness of-fit of the marketing study's model using alpha =.05

Answer 1

A survey of 500 customers finds the following: 175 prefer Calvin Klein, 150 prefer Tommy Hilfiger, 150 Prefer Ralph Lauren and 25 prefer other.

Store marketing study claims 40% of customers prefer Calvin Klein, 30% prefer Tommy Hilfiger, 20% prefer Ralph Lauren and 10% prefer other.

I find expected customer number of calvin klein = 500 *40 /100 = 200 .

similarly I find for all the other brands as summarized below-

Brand	Observed frequency	Expected frequency
Calvin Klein	175	200
Hilfiger	150	150
Ralph Lauren	150	100
other	25	50

I shall test for 2 ( Chi Square ) goodness of fit.

2 = ( Observed - Expected )2 / Expected

= (175 -200)^2 / 200 + ( 150 - 150)^2 / 150 + ( 150-100)^2 / 100+ ( 25-50 ) ^ 2 / 50 = 40.625

2 crit = 2 =0.05 , 3  = 7.815 [ since there are 4 groups so 3 degrees of freedom]

2 crit   < 2  so reject null hypothesis.

Data doesn't fit well with the study claim.

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