With double-digit annual percentage increase in the cost of health insurance, mo
ID: 3258000 • Letter: W
Question
With double-digit annual percentage increase in the cost of health insurance, more and more workers are likely to lack health insurance coverage. 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 companies. Sample data are reported for 50 employees of small companies, 75 employees for 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 =0.05=0.05.
a. The value of the 22 test statistic (to 2 decimals).
Answer
b. The p-value is Answerless than 0.005between 0.005 and 0.01between 0.01 and 0.025between 0.025 and 0.05between 0.05 and 0.10greater than 0.10
c. What is your conclusion?
AnswerConclude 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.
d. 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. (0 decimals).
Small: Answer%
Medium: Answer%
Large: Answer%
e. Based on the percentages calculated above, what can you conclude?
AnswerLarge companies have a higher percentage of no coverage than medium and small companies.Medium 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 companies.Small, medium and large companies all have roughly the same percentage of no coverage.
Health Insurance Size of Company Yes No Total Small 30 20 50 Medium 61 14 75 Large 89 11 100Explanation / Answer
The statistical software output for the given problem is:
Chi-Square test:
Hence,
a) X2 = 17.65
b) P - value is less than 0.005
c) Conclude health insurance coverage is not independent of the size of the company.
d) Small = 20/50 = 40%
Medium = 14/75 = 19%
Large = 11/100 = 11%
e) Small companies have a higher percentage of no coverage than large and medium companies.
Statistic DF Value P-value Chi-square 2 17.645833 0.0001Related Questions
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