MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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## Hypothesis Testing and Confidence Interval Example

### Scenario
A proponent of a new proposition on a ballot aims to predict whether the proposition is likely to pass, requiring more than 50% of the votes. A poll is conducted, in which 589 out of 1000 randomly selected people express support.

**Question:** Should the proponent use a hypothesis test or a confidence interval to evaluate the likelihood of passage?

### Hypothesis Testing
1. **Null and Alternative Hypotheses Options:**
   - Option A: 
     - \( H_0: p = \square \)
     - \( H_1: p < \square \)
   - Option B:
     - \( H_0: p = \square \)
     - \( H_1: p > \square \)
   - Option C: 
     - \( H_0: p = \square \)
     - \( H_1: p \neq \square \)
   - Option D:
     - \( H_0: p = \square \)
     - \( H_1: p < \square \)
   - Option E:
     - \( H_0: p = \square \)
     - \( H_1: p > \square \)
   - Option F:
     - A hypothesis test is not appropriate; use a confidence interval.

2. **Finding the Test Statistic:**
   - If hypothesis testing is appropriate:
     - \( z = \square \) (round to two decimal places as needed).

3. **P-Value Options:**
   - \( p\text{-value} = \square \) (round to three decimal places as needed).
   - A hypothesis test is not appropriate; use a confidence interval.

4. **Conclusion Options:**
   - Don't reject \( H_0 \): Not enough evidence to conclude passage.
   - Reject \( H_0 \): Evidence indicates passage.
   - Don't reject \( H_0 \): Enough evidence indicates passage.
   - Conclusion depends on hypothesis testing or confidence interval.

### Confidence Interval
- Construct a 95% confidence interval for the population proportion \( p \):
  - \(( \, , \, )\) (round to two decimal places as needed).
  - A hypothesis test is a more appropriate tool.

### Teaching Points
- Selecting between hypothesis testing and confidence interval depends on the specific inquiry.
- Proper rounding is vital for precision
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Transcribed Image Text:## Hypothesis Testing and Confidence Interval Example ### Scenario A proponent of a new proposition on a ballot aims to predict whether the proposition is likely to pass, requiring more than 50% of the votes. A poll is conducted, in which 589 out of 1000 randomly selected people express support. **Question:** Should the proponent use a hypothesis test or a confidence interval to evaluate the likelihood of passage? ### Hypothesis Testing 1. **Null and Alternative Hypotheses Options:** - Option A: - \( H_0: p = \square \) - \( H_1: p < \square \) - Option B: - \( H_0: p = \square \) - \( H_1: p > \square \) - Option C: - \( H_0: p = \square \) - \( H_1: p \neq \square \) - Option D: - \( H_0: p = \square \) - \( H_1: p < \square \) - Option E: - \( H_0: p = \square \) - \( H_1: p > \square \) - Option F: - A hypothesis test is not appropriate; use a confidence interval. 2. **Finding the Test Statistic:** - If hypothesis testing is appropriate: - \( z = \square \) (round to two decimal places as needed). 3. **P-Value Options:** - \( p\text{-value} = \square \) (round to three decimal places as needed). - A hypothesis test is not appropriate; use a confidence interval. 4. **Conclusion Options:** - Don't reject \( H_0 \): Not enough evidence to conclude passage. - Reject \( H_0 \): Evidence indicates passage. - Don't reject \( H_0 \): Enough evidence indicates passage. - Conclusion depends on hypothesis testing or confidence interval. ### Confidence Interval - Construct a 95% confidence interval for the population proportion \( p \): - \(( \, , \, )\) (round to two decimal places as needed). - A hypothesis test is a more appropriate tool. ### Teaching Points - Selecting between hypothesis testing and confidence interval depends on the specific inquiry. - Proper rounding is vital for precision
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