5. A market researcher wants to determine if the shape of a client\'s packaging

Question

5. A market researcher wants to determine if the shape of a client's packaging material is an important factor in a consumer's selection of the product. The researcher randomly selects 2000 consumers and gives each of them five differently shaped packages of the same product. One month later each consumer is asked to indicate a preference for one of the shaped packages. The results of the survey are given in the table below Shape of the Package #2 450 #1 #3 #4 #5 385 # of Customers Selecting the Package 430 365 370 Use a Chi Square Goodness-of-Fit Test to test the null hypothesis that sample data fits a uniform distribution at a- 1%. Can you conclude that the sample data indicates a preference for packaging shape?

Explanation / Answer

Ho: sample data fits a uniform distribution i.e., no preference for packaging shape

H1: Sample data indicates a preference for packaging shape.

Here, Chi-square calculated value is greater than Chi-square critical/tablulated value. So we reject null hypothesis i.e., sample data indicates a preference for packaging shape.

So, Client's packaging material is an important factor in consumer selection of a product.

Oi Ei Oi-Ei (Oi-Ei)^2 ((Oi-Ei)^2)/Ei 430 400 30 900 2.25 450 400 50 2500 6.25 385 400 -15 225 0.5625 365 400 -35 1225 3.0625 370 400 -30 900 2.25

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