MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Understanding Hypothesis Testing: A Case Study**
**Context:**
Among college students, the proportion who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of campus debates, a political scientist claims that the proportion of college students who are interested is more than 65%. A poll of 255 college students found that 169 say they’re interested in their district’s election results. The question is whether there is enough evidence to support the scientist’s claim at the 0.05 level of significance.
**Steps for Hypothesis Testing:**
1. **State the Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p = 0.65 \)
- Alternative Hypothesis (\( H_1 \)): \( p > 0.65 \)
2. **Determine the Type of Test Statistic to Use:**
- Use a z-test for proportions.
3. **Calculate the Test Statistic:**
- Use the formula for the z-test statistic for proportions:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}
\]
- \(\hat{p}\) is the sample proportion = \(\frac{169}{255}\)
- \(p_0\) is the hypothesized population proportion = 0.65
- \(n\) is the sample size = 255
4. **Find the p-value:**
- Find the probability that the calculated z-value would occur under the null hypothesis.
- Use statistical software or z-tables for precise values.
5. **Draw a Conclusion:**
- If the p-value is less than the significance level (0.05), reject the null hypothesis.
- Answer whether there is enough evidence to support the claim that more than 65% of students are interested in the election results.
**Decision Box:**
- Yes/No selection to confirm if there is evidence to support the claim.
**Icons Usage:**
- There are icons for basic statistical symbols such as mean (\(\mu\)), standard deviation (\(\sigma\)), sample mean (\(\bar{x}\)), sample size (\(n\)), and proportion (\(p\)) to assist in visual understanding and calculations.
By working through this example, students can learn how to apply hypothesis testing](https://content.bartleby.com/qna-images/question/5db6d82f-0d7b-4a27-9056-ef6822baa75c/64e8e90b-339b-4931-a0b1-3d416731bd45/mhscq7r_processed.jpeg)
Transcribed Image Text:---
**Understanding Hypothesis Testing: A Case Study**
**Context:**
Among college students, the proportion who say they’re interested in their congressional district’s election results has traditionally been 65%. After a series of campus debates, a political scientist claims that the proportion of college students who are interested is more than 65%. A poll of 255 college students found that 169 say they’re interested in their district’s election results. The question is whether there is enough evidence to support the scientist’s claim at the 0.05 level of significance.
**Steps for Hypothesis Testing:**
1. **State the Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p = 0.65 \)
- Alternative Hypothesis (\( H_1 \)): \( p > 0.65 \)
2. **Determine the Type of Test Statistic to Use:**
- Use a z-test for proportions.
3. **Calculate the Test Statistic:**
- Use the formula for the z-test statistic for proportions:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}
\]
- \(\hat{p}\) is the sample proportion = \(\frac{169}{255}\)
- \(p_0\) is the hypothesized population proportion = 0.65
- \(n\) is the sample size = 255
4. **Find the p-value:**
- Find the probability that the calculated z-value would occur under the null hypothesis.
- Use statistical software or z-tables for precise values.
5. **Draw a Conclusion:**
- If the p-value is less than the significance level (0.05), reject the null hypothesis.
- Answer whether there is enough evidence to support the claim that more than 65% of students are interested in the election results.
**Decision Box:**
- Yes/No selection to confirm if there is evidence to support the claim.
**Icons Usage:**
- There are icons for basic statistical symbols such as mean (\(\mu\)), standard deviation (\(\sigma\)), sample mean (\(\bar{x}\)), sample size (\(n\)), and proportion (\(p\)) to assist in visual understanding and calculations.
By working through this example, students can learn how to apply hypothesis testing
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