Critical values for quick reference during this activity. Confidence level Critical value 0.90 z* = 1.645 0.95 z* = 1.960 0.99 z* = 2.576 Jump to level 1 In a poll of 1000 randomly selected voters in a local election, 778 voters were against fire department bond measures. What is the sample proportion p? Ex: 0.123 What is the margin of error m for the 99% confidence level? Ex: 0.123

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Author:Amos Gilat
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### Critical Values for Quick Reference During This Activity

| Confidence Level | Critical Value             |
|------------------|----------------------------|
| 0.90             | \( z^* = 1.645 \)          |
| 0.95             | \( z^* = 1.960 \)          |
| 0.99             | \( z^* = 2.576 \)          |

### Example Problem

**Jump to level 1**

In a poll of **1000** randomly selected voters in a local election, **778** voters were against fire department bond measures.

**Questions:**

1. What is the sample proportion \( \hat{p} \)?
    - **Input Format:** Ex: 0.123

2. What is the margin of error \( m \) for the **99% confidence level**?
    - **Input Format:** Ex: 0.123

### Graphical Explanation

There is a table presented above containing critical values for different confidence levels (0.90, 0.95, and 0.99). These values (\( z^* \)) are necessary for calculating confidence intervals in statistical analysis. The critical values for the given confidence levels are:
- **0.90:** \( z^* = 1.645 \)
- **0.95:** \( z^* = 1.960 \)
- **0.99:** \( z^* = 2.576 \)

These values help to determine the z-scores, which are then used to calculate the margin of error, and subsequently, the confidence intervals for estimating population parameters.
Transcribed Image Text:### Critical Values for Quick Reference During This Activity | Confidence Level | Critical Value | |------------------|----------------------------| | 0.90 | \( z^* = 1.645 \) | | 0.95 | \( z^* = 1.960 \) | | 0.99 | \( z^* = 2.576 \) | ### Example Problem **Jump to level 1** In a poll of **1000** randomly selected voters in a local election, **778** voters were against fire department bond measures. **Questions:** 1. What is the sample proportion \( \hat{p} \)? - **Input Format:** Ex: 0.123 2. What is the margin of error \( m \) for the **99% confidence level**? - **Input Format:** Ex: 0.123 ### Graphical Explanation There is a table presented above containing critical values for different confidence levels (0.90, 0.95, and 0.99). These values (\( z^* \)) are necessary for calculating confidence intervals in statistical analysis. The critical values for the given confidence levels are: - **0.90:** \( z^* = 1.645 \) - **0.95:** \( z^* = 1.960 \) - **0.99:** \( z^* = 2.576 \) These values help to determine the z-scores, which are then used to calculate the margin of error, and subsequently, the confidence intervals for estimating population parameters.
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