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 65 10 75 Large 88 12 100

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.

1. Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use  = .05. Use Table 12.4.
   
   Compute the value of the  ² test statistic (to 2 decimals).
   
   
   The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
   
   What is your conclusion?
   SelectConclude 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 3
   
2. 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?

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 35   15 50

Medium 67 8 75

Large 87 13 100

a.) 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 test statistic (to 2 decimals).

b.) the p-value is _____________

c.) What is your conclusion _________________

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 (to the nearest whole number).

Small _____ %

Medium ______ %

Large ______ %

Based on the percentages above what do you conclude ___________________

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 32 18 50 Medium 61 14 75 Large 87 13 100

a) Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05. Use Table 12.4.

Compute the value of the 2 test statistic (to 2 decimals). The p value is What is your conclusion?

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 %

Based on the percentages calculated above, what can you conclude?

• Check My Work

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.

1. Compute the X²  test statistic:

2. What is the P-Value? (Using a Chi-Square table)

3.What can we conclude?

4. 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).

5. Based on the Calculated percentages, what can we conclude?

3. 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 α = .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.

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 31 19 50 Medium 68 7 75 Large 90 10 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05. Use Table 12.4. 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?

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.

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 x² test statistic (to 2 decimals).

Find the p-value

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?