With double-digit annual percentage increases in the cost of health insurance, m

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.

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 2 test statistic (to 2 decimals).


The p value is

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).

Health Insurance Size of Company Yes No Total Small 40 10 50 Medium 68 7 75 Large 90 10 100

Explanation / Answer

H0: employee health insurance coverage is independent of the size of the company

H1: employee health insurance coverage is not independent of the size of the company

alpha:5%

Test statistic:

chi square=3.914

P value= 0.58225

P value >0.05, we do not reject the H0. Hence claim is not significant

Oi ei (oi-ei)^2/ei 40 44 0.363636 10 6 2.666667 50 50 0 68 66 0.060606 7 9 0.444444 75 75 0 90 88 0.045455 10 12 0.333333 100 100 0

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