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	39	11	50
	Medium	70	5	75
	Large	89	11	100

1. 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.
   
   Compute the value of the x² test statistic (to 2 decimals).?
   
   
   The p value is ?
   
   What is your conclusion?
   Conclude health insurance coverage is not independent of the size of the company/Cannot reject the assumption that health insurance coverage and size of the company are independent
2. 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	%

   
   
   Based on the percentages calculated above, what can you conclude?

Answer 1

a) applying chi square test:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	small	44.000	6.000	50
	medium	66.000	9.000	75
	large	88.000	12.000	100
	total	198	27	225
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	small	0.5682	4.1667	4.735
	medium	0.2424	1.7778	2.020
	large	0.0114	0.0833	0.095
	total	0.822	6.028	6.850

chi square test statistic X² =6.850

p value =0.0326

Conclude health insurance coverage is not independent of the size of the company

b)

small	22%
medium	7%
large	11%

we can conclude that smaller companies are most likely to lack health insurance coverage.