With double-digit annual percentage increases in the cost of health insurance, m
ID: 3321670 • 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. Health Insurance Size of Company Yes No Total Small 36 14 50 Medium 68 7 75 Large 85 15 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05. Compute the value of the 2 test statistic (to 2 decimals). The p value is What is your conclusion? 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?
Explanation / Answer
Result:
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 36 14 50
Medium 68 7 75
Large 85 15 100
Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
Compute the value of the 2 test statistic 7.91 (to 2 decimals).
The p value is 0.0191
What is your conclusion?
O is rejected.
The employee health insurance coverage is not independent of the size of the company.
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 28% Medium 9% Large 15% Based on the percentages calculated above, what can you conclude?
The data support the article that employees of small companies are more likely to lack health insurance coverage.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
yes
no
Total
fo-fe
small
36
14
50
-6
6
medium
68
7
75
5
-5
large
85
15
100
1
-1
Total
189
36
225
Expected Frequencies
Column variable
Row variable
yes
no
Total
(fo-fe)^2/fe
small
42
8
50
0.8571
4.5000
medium
63
12
75
0.3968
2.0833
large
84
16
100
0.0119
0.0625
Total
189
36
225
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.9915
Chi-Square Test Statistic
7.9117
p-Value
0.0191
Reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
yes
no
Total
fo-fe
small
36
14
50
-6
6
medium
68
7
75
5
-5
large
85
15
100
1
-1
Total
189
36
225
Expected Frequencies
Column variable
Row variable
yes
no
Total
(fo-fe)^2/fe
small
42
8
50
0.8571
4.5000
medium
63
12
75
0.3968
2.0833
large
84
16
100
0.0119
0.0625
Total
189
36
225
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.9915
Chi-Square Test Statistic
7.9117
p-Value
0.0191
Reject the null hypothesis
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