Question

. A manager for an insurance company believes that customers have the following preferences for life insurance products: 40% prefer Whole Life, 10% prefer Universal Life, and 50% prefer Life Annuities. The results of a survey of 310 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 Whole 124 Universal 31 Annuities 155

State the null and alternative hypothesis.

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

State the null and alternative hypothesis in terms of the expected proportions for each category.

Find the value of the test statistic. Round your answer to three decimal places.

Find the degrees of freedom associated with the test statistic for this problem.

Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance.

State the conclusion of the hypothesis test at the 0.025 level of significance.  

Answer 1

W do a goodness of fit test here.

The Hypothesis:

H0: The proportions are the same as its hypothesized values.

Ha: At least one of the proportions differs from its hypothesiszed value.

The Test Statistic: Each expected value = (Expected %/100) * Total Population.

Product #	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Whole Life	124	40	124	0	0
Universal Life	31	10	31	0	0
Life Annuities	155	50	155	0	0
Total	310.00	100.00	310.00	0.00	0.000

= 0.000

The Degrees of Freedom: (df) is = n - 1 = 3 - 1 = 2

The Critical Value: For = 0.025, df = 2; critical value = 7.378

The Decision Rule: If test is > critical, Then reject H0.

The Decision: Since If test (0.000) is < critical (7.378), We fail to reject H0.

The Conclusion: There is insufficient evidence at the 97.5% significance level to conclude that at least one of the proportions differs from its hypothesiszed value.