With double-digit annual percentage increases in the cost of health insurance, m
ID: 3154650 • 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 (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.
a) Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use a = .05. Compute the value of the X 2 test statistic (to 2 decimals): ________. The p-value is ______. What is your conclusion?
- Select your answer -Conclude 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
b) 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= ? %
c) Based on the percentages calculated above, what can you conclude?
Health Insurance Size of company Yes No Total Small 40 10 50 Medium 68 7 75 Large 90 10 100a) Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use a = .05. Compute the value of the X 2 test statistic (to 2 decimals): ________. The p-value is ______. What is your conclusion?
- Select your answer -Conclude 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
b) 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= ? %
c) Based on the percentages calculated above, what can you conclude?
Explanation / Answer
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.
Compute the value of the X 2 test statistic (to 2 decimals): 3.91 .
The p-value is 0.1413. What is your conclusion?
Do not reject the null hypothesis because P=0.1413 > 0.05 level of significance.
- Select your answer –
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
b) 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= 20%
Medium= 9 %
Large= 10%
c) Based on the percentages calculated above, what can you conclude?
Based on company size percentages, employees of small companies are more likely to lack health insurance coverage.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Size of company
Yes
No
Total
fo-fe
Small
40
10
50
-4
4
Medium
68
7
75
2
-2
Large
90
10
100
2
-2
Total
198
27
225
Expected Frequencies
Column variable
Size of company
Yes
No
Total
(fo-fe)^2/fe
Small
44
6
50
0.3636
2.6667
Medium
66
9
75
0.0606
0.4444
Large
88
12
100
0.0455
0.3333
Total
198
27
225
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991465
Chi-Square Test Statistic
3.914141
p-Value
0.1413
Do not reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Size of company
Yes
No
Total
fo-fe
Small
40
10
50
-4
4
Medium
68
7
75
2
-2
Large
90
10
100
2
-2
Total
198
27
225
Expected Frequencies
Column variable
Size of company
Yes
No
Total
(fo-fe)^2/fe
Small
44
6
50
0.3636
2.6667
Medium
66
9
75
0.0606
0.4444
Large
88
12
100
0.0455
0.3333
Total
198
27
225
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991465
Chi-Square Test Statistic
3.914141
p-Value
0.1413
Do not reject the null hypothesis
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