Test the independence of attributes.
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 principle of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 99 employees, and large companies are companies that 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.
Statgraphics or Excel is recommended for this problem.
|
Health Insurance
|
|
Size of Company
|
Yes
|
No
|
Total
|
|
Small
|
36
|
14
|
50
|
|
Medium
|
65
|
10
|
75
|
|
Large
|
88
|
12
|
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.
Compute the value of the X2 test statistic (to 2 decimals).
What is the p-value?
What is your conclusion?
b. The USA Today article indicated employees of small companies are most likely to lack health insurance coverage. Calculate the percentage of employees without health insurance based on company size (0 decimals).
Small _____ %
Medium _____ %
large _____ %
founded on the percentages calculated above, what can you bring to a close?