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 Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2  

What is your conclusion?
SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3  

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).

Based on the percentages calculated above, what can you conclude?
SelectLarge companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall companies have a higher percentage of no coverage than large and medium companiesSmall, medium, and large companies all have roughly the same percentage of no coverageItem 7

Health Insurance Size of Company Yes No Total Small 36 14 50 Medium 68 7 75 Large 85 15 100

Explanation / Answer

applying chi square test of independence:

value of the test statistic=7.91

p value is 0.0191

between .01 and .025

Conclude health insurance coverage is not independent of the size of the company

from above:

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

Observed O Yes No Total small 36 14 50 medium 68 7 75 large 85 15 100 Total 189 36 225 Expected E=rowtotal*column total/grand 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 =(O-E)^2/E Yes No Total small 0.8571 4.5000 5.357 medium 0.3968 2.0833 2.480 large 0.0119 0.0625 0.074 Total 1.266 6.646 7.9117

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