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. Size of Company Small Medium Large Health Insurance Yes 31 61 No 19 14 12 Total 50 75 100 a. Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use α = .05. Use Table 12.4. Compute the value of the χ test statistic (to 2 decimals). The p value is Select What is your conclusion? Select 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 Based on the Select s calculated above, what can you conclude?

Answer 1

a) applying chi square test:

Observed	Oi	yes	no	Total
	small	31	19	50
	medium	61	14	75
	large	88	12	100
	total	180	45	225
Expected	Ei=row total*column total/grand total	yes	no	Total
	small	40.00	10.00	50
	medium	60.00	15.00	75
	large	80.00	20.00	100
	total	180	45	225
chi square    χ2	=(Oi-Ei)2/Ei	yes	no	Total
	small	2.0250	8.1000	10.125
	medium	0.0167	0.0667	0.083
	large	0.8000	3.2000	4.000
	total	2.842	11.367	14.208

test statistic X² =14.21

p value =0.001

conclusion:reject Ho ; conclude health insurance coverage is dependent on size of the company

b)

snall	38%
medium	19%
large	12%