Health insurance benetits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company. Health Insurance Size of Company Yes No Total Small 40 10 50 Medium 63 12 75 Large 86 14 100 a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-

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### Health Insurance Benefits and Company Size

Health insurance benefits vary by the size of the company. The data below, adapted from the Henry J. Kaiser Family Foundation, show the number of companies providing health insurance for small, medium, and large companies. For this study:

- **Small companies**: Fewer than 100 employees.
- **Medium companies**: 100 to 999 employees.
- **Large companies**: 1,000 or more employees.

A questionnaire was sent to 225 employees, asking if they had health insurance and to indicate their company's size.

#### Health Insurance Coverage by Company Size:

| Size of Company | Yes (Insurance) | No (Insurance) | Total |
|-----------------|-----------------|----------------|-------|
| Small           | 40              | 10             | 50    |
| Medium          | 63              | 12             | 75    |
| Large           | 86              | 14             | 100   |

---

#### a. Test of Independence

Conduct a test to determine whether health insurance coverage is independent of company size.

- **What is the p-value?**  
  The p-value is greater than 0.10.

- **Conclusion with α = 0.05**  
  Cannot reject the assumption that health insurance coverage and company size are independent.

---

#### b. Health Insurance Coverage by Company Size

Calculate the percentage of employees without health insurance for each company size:

- **Small Companies**: Calculate \( \frac{10}{50} \times 100 \% \).
- **Medium Companies**: Calculate \( \frac{12}{75} \times 100 \% \).
- **Large Companies**: Calculate \( \frac{14}{100} \times 100 \% \).

This information helps in understanding the likelihood of employees lacking health insurance based on company size.
Transcribed Image Text:### Health Insurance Benefits and Company Size Health insurance benefits vary by the size of the company. The data below, adapted from the Henry J. Kaiser Family Foundation, show the number of companies providing health insurance for small, medium, and large companies. For this study: - **Small companies**: Fewer than 100 employees. - **Medium companies**: 100 to 999 employees. - **Large companies**: 1,000 or more employees. A questionnaire was sent to 225 employees, asking if they had health insurance and to indicate their company's size. #### Health Insurance Coverage by Company Size: | Size of Company | Yes (Insurance) | No (Insurance) | Total | |-----------------|-----------------|----------------|-------| | Small | 40 | 10 | 50 | | Medium | 63 | 12 | 75 | | Large | 86 | 14 | 100 | --- #### a. Test of Independence Conduct a test to determine whether health insurance coverage is independent of company size. - **What is the p-value?** The p-value is greater than 0.10. - **Conclusion with α = 0.05** Cannot reject the assumption that health insurance coverage and company size are independent. --- #### b. Health Insurance Coverage by Company Size Calculate the percentage of employees without health insurance for each company size: - **Small Companies**: Calculate \( \frac{10}{50} \times 100 \% \). - **Medium Companies**: Calculate \( \frac{12}{75} \times 100 \% \). - **Large Companies**: Calculate \( \frac{14}{100} \times 100 \% \). This information helps in understanding the likelihood of employees lacking health insurance based on company size.
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