1. With double- digit annual percentage increases in the cost of health insuranc
ID: 3327550 • Letter: 1
Question
1. 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
a. 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.
b. What is the p-value? What is your conclusion based on p-value approach?
c. 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.
Please tell me exactly what to type in Excel to get these answers and if there are any formulas that can be used to get them. Thanks!
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
Sol:
perform chi sq test for independence
HO:employee health insurance coverage is INDEPENDENT of the size of the company
H1:employee health insurance coverage is DEPENDENTof the size of the company
alpha=0.05
its 2*3 cntingency table
calculate expected frequencies as
E=row total*colum total/grandtotal
Given frequencies are O
chi sq test stat=TOTAL(O-E)^2/E
Degrees of freedom=(r-1)(c-1)
r-rows
c-columns
=(3-1)(2-1)
=2*1
df =2
chi sq critical value=5.99 for 2 df and 0.05 level of significance
chi sq cal>chi sq cri
20.37>5.99
Decison:
Reject Null hypothesis
Accept alternative Hypothesis
Conclusion:
there is no sufficient evidence at 5% level of significance to conlcude thatemployee health insurance coverage is independent of the size of the company
Solutionb:
p=0.0038
p<0.05
Reject Null hypothesis
Accept alternative Hypothesis
Conclusion:
there is no sufficient evidence at 5% level of significance to conlcude thatemployee health insurance coverage is independent of the size of the company
p value=
HEALTHINSURANCE SIZEOFCOMPANY YES NO TOTAL SMALL 50 25 75 MEDIUM 80 20 100 LARGE 115 10 125 TOTAL 245 55 300 CHI SQ STAT CALCULATION O E O-E (O-E)^2 (O-E)^2/E 50 61.25 -11.25 126.5625 2.066327 25 13.75 11.25 126.5625 9.204545 80 81.66667 -1.66667 2.777778 0.034014 20 18.33333 1.666667 2.777778 0.151515 115 102.0833 12.91667 166.8403 1.634354 10 22.91667 -12.9167 166.8403 7.280303 CHISQSTAT 20.37106Related Questions
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