Question

Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the 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 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company Health Insurance Size of Company Yes No Total Small 34 16 50 Medium 67 8 75 Large 88 12 100 a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-value? Compute the value of the y2 test statistic (to 2 decimals). The p-value is less than .005 Using a .05 level of significance, what is your conclusion? Conclude health insurance coverage is not independent of the size of the company b. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number) Small Medium Large Based on the percentages calIcu lated above, what can you conclude? Large companies have a higher percentage of no coverage than medium and small companies

Answer 1

Ans:

a)

	Observed(O)
	Yes	No	Total
small	34	16	50
medium	67	8	75
large	88	12	100
Total	189	36	225
	Expected(E)
	Yes	No	Total
small	42	8	50
medium	63	12	75
large	84	16	100
Total	189	36	225
	Chi square=(O-E)^2/E
	Yes	No	Total
small	1.52	8.00	9.52
medium	0.25	1.33	1.59
large	0.19	1.00	1.19
Total	1.97	10.33	12.30

Test statistic:

Chi square=12.30

df=(3-1)*(2-1)=2

p-value=chidist(12.30,2)=0.0021

p-value is less than 0.005

Conclude that coverage is not independent of the size of the company.

b)

small=100*32/50=16%

medium=100*8/75=11%

large=100*12/100=12%

Small companies have a higher percentage of no coverage than medium and small companies.