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 35   15 50

Medium 67 8 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. Compute the value of the test statistic (to 2 decimals).

b.) the p-value is _____________

c.) What is your conclusion _________________

d.) 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 above what do you conclude ___________________

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	yes	No	Total
	small	42.000	8.000	50.00
	medium	63.000	12.000	75.00
	large	84.000	16.000	100.00
	total	189.00	36.00	225.00
chi square    χ2	=(Oi-Ei)2/Ei	yes	No	Total
	small	1.167	6.125	7.2917
	medium	0.254	1.333	1.5873
	large	0.107	0.563	0.6696
	total	1.5278	8.0208	9.549
test statistic X2 =		9.55

b)

p value =

0.008    or less than 0.01

we can conclude that employee health insurance coverage is dependent of the size of the company

d)

small	30%
medium	11%
large	13%

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