Question

A medical researcher claims that 60% of people pay for prescriptions with private insurance, 25% pay with Medicare, and the remaining pay with personal funds. To evaluate this claim, a random sample of 50 people was taken. The sample had the following results: Private Insurance Medicare Personal 32 10 8 What is the test statistic for the test? Round your final answer to two decimals. A

Answer 1

the necessary calculation table :-

	observed	test proportion	expected	(obs — ер)? етр
private insurance	32	0.60	0.60*50 =30	(30-32)2/30 = 0.13333
medicare	10	0.25	0.25*50=12.5	0.5
personal	8	1-(0.60+0.25) = 0.15	0.15*50 =7.5	0.03333
	sum=50			sum = 0.66666

the test statistic for this test be:-

$\chi^2=\sum \frac{(obs-exp)^2}{exp}=0.66666\approx \mathbf{0.67}$

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