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 39 11 50
Medium 70 5 75
Large 89 11 100
  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 x2 test statistic (to 2 decimals).?


    The p value is ?

    What is your conclusion?
    Conclude health insurance coverage is not independent of the size of the company/Cannot reject the assumption that health insurance coverage and size of the company are independent
  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

a) applying chi square test:

Expected Ei=row total*column total/grand total Yes No Total
small 44.000 6.000 50
medium 66.000 9.000 75
large 88.000 12.000 100
total 198 27 225
chi square    χ2 =(Oi-Ei)2/Ei Yes No Total
small 0.5682 4.1667 4.735
medium 0.2424 1.7778 2.020
large 0.0114 0.0833 0.095
total 0.822 6.028 6.850

chi square test statistic X2 =6.850

p value =0.0326

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

b)

small 22%
medium 7%
large 11%

we can conclude that smaller companies are most likely to lack health insurance coverage.

orchestra answered 2 years ago
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