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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Testing a Claim About the Population Mean**
To test the claim about the population mean \( \mu \) at the significance level \( \alpha \), assume the population is normally distributed.
**Given:**
- Claim: \( \mu < 4815 \)
- Significance level \( \alpha = 0.10 \)
- Sample statistics:
- Sample mean \( \bar{x} = 4917 \)
- Sample standard deviation \( s = 5501 \)
- Sample size \( n = 52 \)
**Steps to Follow:**
1. **State the Null and Alternative Hypotheses:**
- \( H_0: \mu = 4815 \) (Null Hypothesis)
- \( H_1: \mu < 4815 \) (Alternative Hypothesis)
2. **Find the Standardized Test Statistic \( t \):**
- Use the formula for the test statistic in a t-test:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
- Enter the calculated \( t \) value: [Type integers or decimals, do not round]
3. **Round the Test Statistic \( t \) to Two Decimal Places.**
4. **Determine the P-value:**
- Calculate the P-value based on the \( t \)-distribution.
- Enter the calculated P-value: [Round to three decimal places as needed]
5. **Decision:**
- Decide whether to reject or fail to reject the null hypothesis.
- Choose the correct answer:
- [ ] Reject \( H_0 \)
- [ ] Fail to reject \( H_0 \)
**Conclusion:**
Discuss whether there is sufficient evidence at the specified level of significance to support the claim.
**Note:**
Each calculation step requires precision, and rounding should be done as specified to ensure accurate results in hypothesis testing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9e160d3-5f97-49cf-bcaa-ed4b67fa5615%2Fb7831d59-5f25-49e1-8390-cf02f9ba96a0%2F53pok4a.jpeg&w=3840&q=75)
Transcribed Image Text:**Testing a Claim About the Population Mean**
To test the claim about the population mean \( \mu \) at the significance level \( \alpha \), assume the population is normally distributed.
**Given:**
- Claim: \( \mu < 4815 \)
- Significance level \( \alpha = 0.10 \)
- Sample statistics:
- Sample mean \( \bar{x} = 4917 \)
- Sample standard deviation \( s = 5501 \)
- Sample size \( n = 52 \)
**Steps to Follow:**
1. **State the Null and Alternative Hypotheses:**
- \( H_0: \mu = 4815 \) (Null Hypothesis)
- \( H_1: \mu < 4815 \) (Alternative Hypothesis)
2. **Find the Standardized Test Statistic \( t \):**
- Use the formula for the test statistic in a t-test:
\[
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
\]
- Enter the calculated \( t \) value: [Type integers or decimals, do not round]
3. **Round the Test Statistic \( t \) to Two Decimal Places.**
4. **Determine the P-value:**
- Calculate the P-value based on the \( t \)-distribution.
- Enter the calculated P-value: [Round to three decimal places as needed]
5. **Decision:**
- Decide whether to reject or fail to reject the null hypothesis.
- Choose the correct answer:
- [ ] Reject \( H_0 \)
- [ ] Fail to reject \( H_0 \)
**Conclusion:**
Discuss whether there is sufficient evidence at the specified level of significance to support the claim.
**Note:**
Each calculation step requires precision, and rounding should be done as specified to ensure accurate results in hypothesis testing.
![### Hypothesis Testing for Population Mean
**Task:**
Test the claim about the population mean \( \mu \) at the level of significance \( \alpha \). Assume the population is normally distributed.
**Given Data:**
- **Claim:** \( \mu < 4815 \), \( \alpha = 0.10 \)
- **Sample Statistics:**
- \(\bar{x} = 4917\)
- \(s = 5501\)
- \(n = 52\)
**Steps to Follow:**
1. **Formulate Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( \mu = 4815 \)
- **Alternative Hypothesis (\(H_a\))**: \( \mu < 4815 \)
2. **Find the standardized test statistic \( t \):**
- Use the formula for the t-statistic in hypothesis testing for a population mean:
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
- (Round to two decimal places as needed.)
3. **Determine the P-value:**
- The P-value needs to be calculated based on the t-statistic.
- (Round to three decimal places as needed.)
**Note:**
This process involves calculating the test statistic and obtaining the P-value to make a decision on whether to reject the null hypothesis \(H_0\) in favor of the alternative hypothesis \(H_a\), based on the given level of significance \( \alpha = 0.10 \). If the P-value is less than \( \alpha \), reject \(H_0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9e160d3-5f97-49cf-bcaa-ed4b67fa5615%2Fb7831d59-5f25-49e1-8390-cf02f9ba96a0%2Fqio9o5.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Population Mean
**Task:**
Test the claim about the population mean \( \mu \) at the level of significance \( \alpha \). Assume the population is normally distributed.
**Given Data:**
- **Claim:** \( \mu < 4815 \), \( \alpha = 0.10 \)
- **Sample Statistics:**
- \(\bar{x} = 4917\)
- \(s = 5501\)
- \(n = 52\)
**Steps to Follow:**
1. **Formulate Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( \mu = 4815 \)
- **Alternative Hypothesis (\(H_a\))**: \( \mu < 4815 \)
2. **Find the standardized test statistic \( t \):**
- Use the formula for the t-statistic in hypothesis testing for a population mean:
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
- (Round to two decimal places as needed.)
3. **Determine the P-value:**
- The P-value needs to be calculated based on the t-statistic.
- (Round to three decimal places as needed.)
**Note:**
This process involves calculating the test statistic and obtaining the P-value to make a decision on whether to reject the null hypothesis \(H_0\) in favor of the alternative hypothesis \(H_a\), based on the given level of significance \( \alpha = 0.10 \). If the P-value is less than \( \alpha \), reject \(H_0\).
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