Question

With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.

		Health Insurance
	Size of Company	Yes	No	Total
	Small	38	12	50
	Medium	62	13	75
	Large	89	11	100

Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use  = .05. Use Table 12.4.

A.) Compute the value of the  2 test statistic (to 2 decimals).

B.) The USA Today 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	%

Answer 1

applying chi square test of independence:

Observed	OBS	yes	no	Total
	small	38	12	50
	medium	62	13	75
	large	89	11	100
	Total	189	36	225
Expected	Ei=?row*?column/?total	yes	no	Total
	small	42.000	8.000	50
	medium	63.000	12.000	75
	large	84.000	16.000	100
	Total	189	36	225
chi square	=(Oi-Ei)2/Ei	yes	no	Total
	small	0.38	2.00	2.38
	medium	0.02	0.083	0.10
	large	0.30	1.563	1.86
	Total	0.69	3.65	4.340

test statsistic =4.34

b)

dividing each no cell with its row total:

percentages of employees without health insurance based on company size is given below

small	24.0%
medium	17%
large	11.0%