Question

Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1,000 or more employees.

The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.

Health Insurance	Size of the Company
	Small	Medium	Large
Yes	36	65	88
No	14	10	12

(a) Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company.

State the null and alternative hypotheses.

H₀: Having health insurance is independent of the size of the company.
H_a: Having health insurance is not independent of the size of the company. CORRECT!!

Find the value of the test statistic. (Round your answer to three decimal places.)

Answer 1

Given Total 189 X Y Total Small 36 14 50 Medium 65 10 75 Large 88 12 100 36 225 Eexpected values = (Row total x column total)/N A B C T X Y 42.00 8.00 63.00 12.00 84.00 16.00 Chi-square distribution table Observed Expected Chi square (O) (E) =(O-E)?/E 36 42.0000 0.8571 65 63.0000 0.0635 88 84.0000 0.1905 14 8.0000 4.5000 10 12.0000 0.3333 12 16.0000 1.0000 6.9444 Test statistic x2 = E(0=83) = 6.944

Test hypothesis are Null hypothesis Ho: The health insurance coverage is independent of the size of the company Alternatehypothesis Hį: The health insurance coverage is not independent of the size of the company Degrees of fredom (df) df=(r-1) (C-1) = 2 0.05 Critical value 7c 5.991 Test statistic = 6.944 P-value p-value 0.0311 Result Since p-value < 0.05 hence reject the null hypothesis