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	Health Insurance-Yes	Health Insurance-No	Total
Small	39	11	50
Medium	62	13	75
Large	88	12	100

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

Compute the value of the x² test statistic (to 2 decimals).

Find the p-value

What is your conclusion?

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

Ans:

a)

	Observed(O)
Size of Company	Health Insurance-Yes	Health Insurance-No	Total
Small	39	11	50
Medium	62	13	75
Large	88	12	100
Total	189	36	225
	Expected(E)
Size of Company	Health Insurance-Yes	Health Insurance-No	Total
Small	42.00	8.00	50
Medium	63.00	12.00	75
Large	84.00	16.00	100
Total	189.00	36.00	225.00
	Chi square=(O-E)^2/E
Size of Company	Health Insurance-Yes	Health Insurance-No	Total
Small	0.21	1.13	1.34
Medium	0.02	0.08	0.10
Large	0.19	1.00	1.19
Total	0.42	2.21	2.63

Test statistic:

Chi square=2.63

df=(3-1)*(2-1)=2

p-value=CHIDIST(2.63,2)=0.2685

Fail to reject the null hypothesis.There is not sufficient evidence to conclude that employee health insurance coverage is not independent of the size of the company.

Small=100*11/50=22%

Medium=100*13/75=17%

Large=100*12/100=12%

Based on the percentages calculated above,we can say that employees of small companies are more likely to lack health insurance coverage.