C2. Average years of education are reported by social class based on data from the GSS 2018. Mean Standard Deviation Lower class 12.19 3.08 102 Working class 13.16 2.93 523 Middle class 14.60 2.88 498 Upper class 15.21 3.01 34 a. Construct the 95% confidence interval for the mean number of years of education for lower- and working-class respondents. b. Construct the 99% confidence interval for the mean number of years of education for lower-class and middle-class respondents. C. As our confidence in the result increases, how does the size of the confidence interval Change? Explain why this is so.

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**Title: Educational Attainment by Social Class Based on GSS 2018 Data**

---

**Text:**

This section explores the average years of education reported by different social classes, as gathered from the General Social Survey (GSS) 2018.

**Table: Average Years of Education by Social Class**

| Social Class  | Mean | Standard Deviation | N   |
|---------------|------|--------------------|-----|
| Lower class   | 12.19| 3.08               | 102 |
| Working class | 13.16| 2.93               | 523 |
| Middle class  | 14.60| 2.88               | 498 |
| Upper class   | 15.21| 3.01               | 34  |

- **Mean**: The average number of years of education completed.
- **Standard Deviation**: A measure of the amount of variation or dispersion of educational years within each class.
- **N**: The number of respondents in each social class.

**Exercises:**

a. Construct the 95% confidence interval for the mean number of years of education for lower- and working-class respondents.

b. Construct the 99% confidence interval for the mean number of years of education for lower-class and middle-class respondents.

c. As our confidence in the result increases, how does the size of the confidence interval change? Explain why this is so.

---

**Explanation of Exercises:**

- **Confidence Interval**: This is a range of values that is likely to contain the true mean of the population with a certain level of confidence (e.g., 95% or 99%).
- A higher confidence level, such as 99%, will result in a wider confidence interval compared to a lower level, like 95%. This occurs because more certainty requires accounting for more variability, thus expanding the interval to ensure it captures the true mean.

This data provides insights into educational disparities among different social classes and serves as a foundation for statistical analysis exercises involving confidence intervals.
Transcribed Image Text:**Title: Educational Attainment by Social Class Based on GSS 2018 Data** --- **Text:** This section explores the average years of education reported by different social classes, as gathered from the General Social Survey (GSS) 2018. **Table: Average Years of Education by Social Class** | Social Class | Mean | Standard Deviation | N | |---------------|------|--------------------|-----| | Lower class | 12.19| 3.08 | 102 | | Working class | 13.16| 2.93 | 523 | | Middle class | 14.60| 2.88 | 498 | | Upper class | 15.21| 3.01 | 34 | - **Mean**: The average number of years of education completed. - **Standard Deviation**: A measure of the amount of variation or dispersion of educational years within each class. - **N**: The number of respondents in each social class. **Exercises:** a. Construct the 95% confidence interval for the mean number of years of education for lower- and working-class respondents. b. Construct the 99% confidence interval for the mean number of years of education for lower-class and middle-class respondents. c. As our confidence in the result increases, how does the size of the confidence interval change? Explain why this is so. --- **Explanation of Exercises:** - **Confidence Interval**: This is a range of values that is likely to contain the true mean of the population with a certain level of confidence (e.g., 95% or 99%). - A higher confidence level, such as 99%, will result in a wider confidence interval compared to a lower level, like 95%. This occurs because more certainty requires accounting for more variability, thus expanding the interval to ensure it captures the true mean. This data provides insights into educational disparities among different social classes and serves as a foundation for statistical analysis exercises involving confidence intervals.
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