Question

In: Statistics and Probability

With double-digit annual percentage increases in the cost of health insurance, more and more workers are...

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 34 16 50
Medium 67 8 75
Large 88 12 100
  1. 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.

    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
  2. 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 calculated above, what can you conclude?

Solutions

Expert Solution

Applying chi square test of independence:
Expected Ei=row total*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    χ2 =(Oi-Ei)2/Ei yes no Total
small 1.524 8.000 9.5238
medium 0.254 1.333 1.5873
large 0.190 1.000 1.1905
total 1.9683 10.3333 12.3016
test statistic X2 = 12.30

p value is less than 0.005

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

b)

small 32%
medium 11%
large 12%
small companies have a higher percentage of no coverage than large and medium companies

orchestra answered 2 years ago
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