Question

A manager for an insurance company believes that customers have the following preferences for life insurance products: 40% prefer Whole Life, 20% prefer Universal Life, and 40% prefer Life Annuities. The results of a survey of 209 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 86 Universal 54 Annuities 69 Step 4 of 10: Find the expected value for the number of customers who prefer Whole Life. Round your answer to two decimal places. Step 5 of 10: Find the expected value for the number of customers who prefer Universal Life. Round your answer to two decimal places. Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places. Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem. Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places. Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance. Step 10 of 10: State the conclusion of the hypothesis test at the 0.025 level of significance.

Answer 1

Null Hypothesis H0: proportions of customers who prefer each product do not differ from the hypothetiical frequencies.

ALternative Hypothesis H1: the proportions of customers who prefer each product differ from the hypothetical frequencies.

Step 4 and Step 5

Under H0, the expected frequencies are

Product	Obs. Freq ( O)	Proportion p	Exp Freq ( E)
Whole	86	0.40	=209*0.40=83.6
Universal	54	0.20	=209*0.20 =41.8
Annuities	69	0.40	=209*0.40= 83.6
Total	209	1	209

Step 6:

Under H0, the test statistic is

Step 7:

Degrees of Freedom = n-1= 3-1= 2

Step 8: The critical value of chi square for 2 df at 0.025 significance level is 8.764

Step 9 : Since chi square calculated is less than chi square tabulated, Fail to Reject H0

Step 10 : At 0.025 level of significance, we conclude that the proportions of customers who prefer each product do not differ from the hypothetical frequencies.