Match the confidence level with the confidence interval for the population mean. Type the correct letter in each box.

equation editorEquation Editor  1. x⎯⎯⎯±1.282(σn√)

equation editorEquation Editor  2. x⎯⎯⎯±1.96(σn√)

equation editorEquation Editor  3. x⎯⎯⎯±2.575(σn√)



A. 80
%
B. 95
%
C. 99
%

Here are the confidence intervals with their corresponding confidence levels:

1. \( \bar{x} \pm 1.282\left(\frac{\sigma}{\sqrt{n}}\right) \) corresponds to **A. 80%** confidence level.
2. \( \bar{x} \pm 1.96\left(\frac{\sigma}{\sqrt{n}}\right) \) corresponds to **B. 95%** confidence level.
3. \( \bar{x} \pm 2.575\left(\frac{\sigma}{\sqrt{n}}\right) \) corresponds to **C. 99%** confidence level.

### Explanation:
- The **z-score** of 1.282 is associated with an **80% confidence level**.
- The **z-score** of 1.96 is commonly used for a **95% confidence level**.
- The **z-score** of 2.575 is used for a **99% confidence level**.

Would you like a detailed explanation of how these z-scores are derived from the standard normal distribution?

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Here are 5 related questions to explore further:

1. What is the relationship between confidence level and margin of error?
2. How is the confidence interval for a sample proportion calculated?
3. What is the effect of increasing the sample size on the confidence interval?
4. How do you calculate the required sample size for a desired confidence level and margin of error?
5. How do you interpret a 95% confidence interval in practical terms?

**Tip:** Increasing the confidence level widens the confidence interval, while decreasing it makes the interval narrower.

Match the confidence level with the confidence interval for the population mean. Type the correct letter in each box. 

1. x⎯⎯⎯±1.282(σ/√n) 
2. x⎯⎯⎯±1.96(σ/√n) 
3. x⎯⎯⎯±2.575(σ/√n)

A. 80% 
B. 95% 
C. 99%

Understand how to match confidence intervals with confidence levels for a population mean. This problem involves z-scores for 80%, 95%, and 99% confidence levels and applies the formula x̄ ± z(σ/√n). Suitable for college-level statistics students.

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