a manager for an insurance company believes that customers have the following preferences for life insurance products: 50% prefer whole life, 20% prefer universal life, and 30% prefer life annuities. the results of a survey of 300 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 whole150universal60annuities90 step 1 of 10: state the null and alternative hypothesis.

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FAHISKT9087GO FAHISKT9087GO · Answer 1

There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

H0:p1=0.5,p2=0.3,p3=0.2

Ha:At least one proportion is different from the stated proportions.

Null hypothesis indicate that proportions are same as stated.

Product observed(fo) pi Expected(fe) (fo-fe)^2/fe

Whole 74 0.5 154.50 41.943

Universal 71 0.3 92.70 5.080

Annuities 164 0.2 61.80 169.010

Total 309 1 309 216.033

Expected value for the number of customers who prefer Whole Life=309*0.5=154.50

Expected value for the number of customers who prefer Universal Life=309*0.3=92.70

Test statistic:

Chi square=216.033

df=3-1=2

critical Chi square value=CHIINV(0.01,2)=9.210

Reject the null hypothesis

Therefore, There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

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