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. Use Table 12.4.

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

B.) 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 38 12 50 Medium 62 13 75 Large 89 11 100

Explanation / Answer

applying chi square test of independence:

test statsistic =4.34

b)

dividing each no cell with its row total:

percentages of employees without health insurance based on company size is given below

Observed OBS yes no Total small 38 12 50 medium 62 13 75 large 89 11 100 Total 189 36 225 Expected Ei=?row*?column/?total yes no Total small 42.000 8.000 50 medium 63.000 12.000 75 large 84.000 16.000 100 Total 189 36 225 chi square =(Oi-Ei)2/Ei yes no Total small 0.38 2.00 2.38 medium 0.02 0.083 0.10 large 0.30 1.563 1.86 Total 0.69 3.65 4.340

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