Full Answer Section

Trade-Off Between Risk and Precision:

There is a fundamental trade-off between risk and precision when it comes to CIs.

• Reducing Risk (Increasing Confidence Level):Increasing the confidence level narrows the CI, making it less likely to miss the true population parameter. However, this comes at the expense of reduced precision (wider interval).
• Increasing Precision (Reducing Margin of Error):A larger sample size leads to a narrower CI, providing a more precise estimate of the population parameter. However, this reduces the risk of capturing the true parameter if the sample is not representative of the population.

Example: Hispanic Migration and Earnings

Frankfort-Nachmias & Leon-Guerrero (Chapter 7, p. 188) discuss Hispanic migration and earnings. Imagine a study investigates the average annual income of Hispanic immigrants in the US.

• Smaller Sample (Lower Precision):A small sample size might lead to a wider CI, say $40,000 to $60,000. While we are 95% confident the true average income falls within this range, the estimate lacks precision.
• Larger Sample (Higher Precision):A larger sample could result in a narrower CI, like $45,000 to $55,000. We maintain a 95% confidence level, but the estimate is more precise, providing a tighter range for the true average income.

Visualizing the Trade-Off

Magnusson’s web blog (Learning Resources) likely uses visualizations like graphs to depict the relationship between confidence level, sample size, and margin of error. A wider band on the graph would represent a larger CI (lower precision), while a narrower band would indicate a smaller CI (higher precision).

Finding a Quantitative Article

The Course Guide or Assignment Help can point you towards quantitative research articles. Look for studies that report CIs and discuss sample size considerations. For example, a study on the effectiveness of an educational intervention might report the average test score improvement with a 90% CI and explain how sample size was determined.

SPSS and General Social Survey

Using SPSS and the General Social Survey dataset, you can explore CIs for various quantitative variables. Let’s say you’re interested in “educational attainment” (years of education).

1. Calculate Descriptive Statistics:In SPSS, use the “Descriptives” function to get the average years of education and relevant statistics.
2. Estimate Confidence Interval:Look for a function to calculate CIs. SPSS might have a dedicated function or you can use formulas based on the sample size and standard deviation.

By analyzing the CI and sample size, you can understand the precision of the average years of education estimate.

Remember: CIs balance the risk of missing the true population parameter with the precision of the estimate. Finding the right balance depends on the research question and desired level of confidence.