Predicting quit rates in manufacturing. The reasons given by workers for quitting their jobs generally fall into one of two categories: (1) worker quits to seek or take a dif- ferent job, or (2) worker quits to withdraw from the labor force. Economic theory suggests that wages and quit rates are related. The next table lists quit rates (quits per 100 employees) and the average hourly wage in a sample of 15 manufacturing industries. Consider the simple linear regression of quit rate y on average wage x. a. Do the data present sufficient evidence to conclude that average hourly wage rate contributes useful informa- tion for the prediction of quit rates? What does your model suggest about the relationship between quit rates and wages?

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**11.95 Predicting Quit Rates in Manufacturing**

The reasons given by workers for quitting their jobs generally fall into one of two categories: (1) a worker quits to seek or take a different job, or (2) a worker quits to withdraw from the labor force. Economic theory suggests that wages and quit rates are related. The next table lists quit rates (quits per 100 employees) and the average hourly wage in a sample of 15 manufacturing industries. Consider the simple linear regression of quit rate \( y \) on average wage \( x \).

a. Do the data present sufficient evidence to conclude that average hourly wage rate contributes useful information for the prediction of quit rates? What does your model suggest about the relationship between quit rates and wages?
Transcribed Image Text:**11.95 Predicting Quit Rates in Manufacturing** The reasons given by workers for quitting their jobs generally fall into one of two categories: (1) a worker quits to seek or take a different job, or (2) a worker quits to withdraw from the labor force. Economic theory suggests that wages and quit rates are related. The next table lists quit rates (quits per 100 employees) and the average hourly wage in a sample of 15 manufacturing industries. Consider the simple linear regression of quit rate \( y \) on average wage \( x \). a. Do the data present sufficient evidence to conclude that average hourly wage rate contributes useful information for the prediction of quit rates? What does your model suggest about the relationship between quit rates and wages?
**Transcription for Educational Website**

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**Task b: Prediction Interval for Quit Rate**

- Find a 95% prediction interval for the quit rate in an industry with an average hourly wage of $9.00.
- Interpret the result.

**Task c: Confidence Interval for Mean Quit Rate**

- Find a 95% confidence interval for the mean quit rate for industries with an average hourly wage of $9.00.
- Interpret this result.

**Data Table: Industry Quit Rates and Average Wages**

- **Industry Data:**
  - **Industry 1:** Quit Rate = 1.4, Average Wage = $8.20
  - **Industry 2:** Quit Rate = 0.7, Average Wage = $10.35
  - **Industry 3:** Quit Rate = 2.6, Average Wage = $6.18
  - **Industry 4:** Quit Rate = 3.4, Average Wage = $5.37
  - **Industry 5:** Quit Rate = 1.7, Average Wage = $9.94
  - **Industry 6:** Quit Rate = 1.7, Average Wage = $9.11
  - **Industry 7:** Quit Rate = 1.0, Average Wage = $10.59
  - **Industry 8:** Quit Rate = 0.5, Average Wage = $13.29
  - **Industry 9:** Quit Rate = 2.0, Average Wage = $7.99
  - **Industry 10:** Quit Rate = 3.8, Average Wage = $5.54
  - **Industry 11:** Quit Rate = 2.3, Average Wage = $7.50
  - **Industry 12:** Quit Rate = 1.9, Average Wage = $6.43
  - **Industry 13:** Quit Rate = 1.4, Average Wage = $8.83
  - **Industry 14:** Quit Rate = 1.8, Average Wage = $10.93
  - **Industry 15:** Quit Rate = 2.0, Average Wage = $8.80

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**Explanation:**

This table showcases the relationship between quit rates and average hourly wages across various industries. The tasks involve statistical analysis to predict and estimate quit rates for a given wage rate.
Transcribed Image Text:**Transcription for Educational Website** --- **Task b: Prediction Interval for Quit Rate** - Find a 95% prediction interval for the quit rate in an industry with an average hourly wage of $9.00. - Interpret the result. **Task c: Confidence Interval for Mean Quit Rate** - Find a 95% confidence interval for the mean quit rate for industries with an average hourly wage of $9.00. - Interpret this result. **Data Table: Industry Quit Rates and Average Wages** - **Industry Data:** - **Industry 1:** Quit Rate = 1.4, Average Wage = $8.20 - **Industry 2:** Quit Rate = 0.7, Average Wage = $10.35 - **Industry 3:** Quit Rate = 2.6, Average Wage = $6.18 - **Industry 4:** Quit Rate = 3.4, Average Wage = $5.37 - **Industry 5:** Quit Rate = 1.7, Average Wage = $9.94 - **Industry 6:** Quit Rate = 1.7, Average Wage = $9.11 - **Industry 7:** Quit Rate = 1.0, Average Wage = $10.59 - **Industry 8:** Quit Rate = 0.5, Average Wage = $13.29 - **Industry 9:** Quit Rate = 2.0, Average Wage = $7.99 - **Industry 10:** Quit Rate = 3.8, Average Wage = $5.54 - **Industry 11:** Quit Rate = 2.3, Average Wage = $7.50 - **Industry 12:** Quit Rate = 1.9, Average Wage = $6.43 - **Industry 13:** Quit Rate = 1.4, Average Wage = $8.83 - **Industry 14:** Quit Rate = 1.8, Average Wage = $10.93 - **Industry 15:** Quit Rate = 2.0, Average Wage = $8.80 --- **Explanation:** This table showcases the relationship between quit rates and average hourly wages across various industries. The tasks involve statistical analysis to predict and estimate quit rates for a given wage rate.
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