Question

A manager for an insurance company believes that customers have the following preferences for life insurance products: 30% prefer Whole Life, 30% prefer Universal Life, and 40% prefer Life Annuities. The results of a survey of 333 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 110 Universal 105 Annuities 118 Step 7 of 10 : Find the degrees of freedom associated with the test statistic for this problem. Step 8: reject or fail null hypothesis at .01 significance Step 9: State the conclusion of the hypothesis test at .01 level of significance

Answer 1

degree of freedom =categories-1=			2
for 0.01 level and 2 df :crtiical value X2 =				9.210

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
whole	0.300	110.0	99.90	1.01	1.021
universal	0.300	105.0	99.90	0.51	0.260
life annuities	0.400	118.0	133.20	-1.32	1.735
total	1.000	333	333		3.0160
test statistic X2 =		3.0160
p value =		0.2214

Step 7 of 10 :

degree of freedom =categories-1=

2

Step 8:

since test statistic <critical value: fail to reject null hypothesis

Step 9:

we do not have sufficient evidence to refute the sales manager's claimed proportions of customers who prefer each product using the data