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	34	16	50
	Medium	67	8	75
	Large	88	12	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  ² test statistic (to 2 decimals).
   
   
   The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
   
   What is your conclusion?
   SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3
   
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

Applying chi square test of independence:

Expected	Ei=row total*column total/grand 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    χ2	=(Oi-Ei)2/Ei	yes	no	Total
	small	1.524	8.000	9.5238
	medium	0.254	1.333	1.5873
	large	0.190	1.000	1.1905
	total	1.9683	10.3333	12.3016
test statistic X2 =		12.30

p value is less than 0.005

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

b)

small	32%
medium	11%
large	12%

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