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 36 14 50

Medium 66 9   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)

	Observed Frequencies
	0
0	yes	no					Total
small	36	14					50
medium	66	9					75
large	87	13					100
Total	189	36					225
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	yes	no					Total
small	189*50/225=42	36*50/225=8					50
medium	189*75/225=63	36*75/225=12					75
large	189*100/225=84	36*100/225=16					100
Total	189	36					225
	(fo-fe)^2/fe
small	0.857	4.500
medium	0.143	0.750
large	0.1071	0.5625

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   6.92

.........

b)

Level of Significance =   0.05
Number of Rows =   3
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 2- 1 ) =   2
  
p-Value =   0.0314

c)

Decision:    p-value < α , Reject Ho          

conclusion : so it is concluded that  employee health insurance coverage is not independent of the size of the company.

d)

small = 14 / 50 *100 = 28%

medium = 9/75 *100 = 27%

large =13/100 *100 = 13%

large company has less percentage of non insurance peolple while small is having large % of non insurance