
MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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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