Question

A manager for an insurance company believes that customers have the following preferences for life insurance products: 40 % prefer Whole Life, 30% prefer Universal Life, and 30% prefer Life Annuities. The results of a survey of 211 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data? Product Number 77 Whole Universal 77 Annuities 57 Copy Data Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.
Find the test statistic and the critical value.

Answer 1

We use a goodness of fit test

H0: The sample has a distribution which agrees with the expected distribution.

Ha: The sample has a distribution that is different from the expected distribution.

The Test Statistic:

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Whole	77	40	84.4	54.76	0.64880
Universal	77	30	63.3	187.69	2.96510
Annuities	57	30	63.3	39.69	0.62700
Total	211	100	211		4.24

$\chi^2$ Test = 4.24

The critical value for df = n - 1 = 3 - 1 = 2, for Alpha = 0.05 is 5.992

(If required for Alpha = 0.01, then critical value = 9.210)

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Since $\chi^2$ Test < $\chi^2$ Critical, We fail to reject H0.