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 32 18 50 Medium 61 14 75 Large 87 13 100

a) 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 What is your conclusion?

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 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	40.000	10.000	50
	medium	60.000	15.000	75
	Large	80.000	20.000	100
	total	180	45	225
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	small	1.6000	6.4000	8.000
	medium	0.0167	0.0667	0.083
	Large	0.6125	2.4500	3.063
	total	2.229	8.917	11.1458

value of the X² test statistic =11.15

p value =0.0038

Reject HO

b)

small	36%
medium	19%
large	13%

we can conclude that small companies have highest no health coverage