Question

A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Use the chi-square test to test the claim that the probabilities show no preference.

plan	1	2	3	4	5
employee	30	55	32	65	18

Answer 1

Null hypothesis: Ho: All plans have equal preference

Alternate hypothesis: Ha: All plans do not  have equal preference.

degree of freedom =categories-1=			4
for 0.05 level and 4 df :crtiical value X2 =				9.4877
Decision rule: reject Ho if value of test statistic X2>9.488

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	0.200	30	40.00		2.500
2	0.200	55	40.00		5.625
3	0.200	32	40.00		1.600
4	0.200	65	40.00		15.625
5	0.200	18	40.00		12.100
total	1.000	200	200		37.4500
test statistic X2 =		37.450
p value =		0.0000

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that All plans do not  have equal preference.