With double- digit annual percentage increases in the cost of health insurance,
ID: 2924278 • Letter: W
Question
With double- digit annual percentage increases 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 employees. Sample data is reported as follows:
Health Insurance
Size of Company
Yes
No
Total
Small
50
25
75
Medium
80
20
100
Large
115
10
125
Total
245
55
300
Conduct a test of independence using critical-value approach to determine whether employee health insurance coverage is independent of the size of the company. State the Hypotheses and the conclusion. Use = .005.
What is the p-value? What is your conclusion based on p-value approach?
The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion.
Health Insurance
Size of Company
Yes
No
Total
Small
50
25
75
Medium
80
20
100
Large
115
10
125
Total
245
55
300
Explanation / Answer
here null hypothesis: Ho: employee health insurance coverage is independent of the size of the company
alternate hypothesis:Ha: employee health insurance coverage is dependent of the size of the company
here degree of freedom =(number of rows-1)*(number of columns-1)=(3-1)*(2-1)=2
for 2 df and 0.005 level critical value =10.5966
applying chi square test of independence
here test stat =20.371 which is greater then critical value; hence we reject null hypothesis.
we have suffciient evidence to conclude that employee health insurance coverage is dependent of the size of the company
for above test stat and 2 degree of freedom p value =0.0000 ; as p value is lower then 0.005 level ;
we reject null hypothesis.we have suffciient evidence to conclude that employee health insurance coverage is dependent of the size of the company
here for proportion of small companies taking health insurance =25/50=0.5 ~50% whcih is largest among group and from above we have found that insurance coverage is dependent of the size of the company.
hence employees of small companies are more likely to lack health insurance coverage
Observed O yes No Total small 50 25 75 medium 80 20 100 large 115 10 125 Total 245 55 300 Expected E=rowtotal*column total/grand total yes No Total small 61.25 13.75 75 medium 81.67 18.33 100 large 102.08 22.92 125 Total 245 55 300 chi square =(O-E)^2/E yes No Total small 2.0663 9.2045 11.271 medium 0.0340 0.1515 0.186 large 1.6344 7.2803 8.915 Total 3.735 16.636 20.371Related Questions
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