### Hypothesis Testing Example **Objective:** Test the following null hypothesis \( (H_0) \) at a significance level of \( \alpha = 0.005 \). #### Hypotheses: - \( H_0: \mu = 64.5 \) - \( H_a: \mu < 64.5 \) You believe the population is normally distributed and you know the standard deviation is \( \sigma = 14.9 \). You obtain a sample mean \( M = 62 \) for a sample of size \( n = 28 \). 1. **Determine the Critical Value:** - Find the critical value for this test. - **Critical value** box: (Enter answer accurate to three decimal places) 2. **Calculate the Test Statistic:** - Determine the test statistic for this sample. - **Test statistic** box: (Enter answer accurate to three decimal places) 3. **Decision on the Test Statistic:** - Evaluate if the test statistic is: - \( \circ \) in the critical region - \( \circ \) not in the critical region 4. **Conclusion from the Test Statistic:** - Make a decision based on the test statistic: - \( \circ \) reject the null - \( \circ \) accept the null - \( \circ \) fail to reject the null 5. **Final Conclusion:** - Determine the final conclusion of the test: - \( \circ \) There is sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5. - \( \circ \) There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5. - \( \circ \) The sample data support the claim that the population mean is less than 64.5. - \( \circ \) There is not sufficient sample evidence to support the claim that the population mean is less than 64.5.
### Hypothesis Testing Example **Objective:** Test the following null hypothesis \( (H_0) \) at a significance level of \( \alpha = 0.005 \). #### Hypotheses: - \( H_0: \mu = 64.5 \) - \( H_a: \mu < 64.5 \) You believe the population is normally distributed and you know the standard deviation is \( \sigma = 14.9 \). You obtain a sample mean \( M = 62 \) for a sample of size \( n = 28 \). 1. **Determine the Critical Value:** - Find the critical value for this test. - **Critical value** box: (Enter answer accurate to three decimal places) 2. **Calculate the Test Statistic:** - Determine the test statistic for this sample. - **Test statistic** box: (Enter answer accurate to three decimal places) 3. **Decision on the Test Statistic:** - Evaluate if the test statistic is: - \( \circ \) in the critical region - \( \circ \) not in the critical region 4. **Conclusion from the Test Statistic:** - Make a decision based on the test statistic: - \( \circ \) reject the null - \( \circ \) accept the null - \( \circ \) fail to reject the null 5. **Final Conclusion:** - Determine the final conclusion of the test: - \( \circ \) There is sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5. - \( \circ \) There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5. - \( \circ \) The sample data support the claim that the population mean is less than 64.5. - \( \circ \) There is not sufficient sample evidence to support the claim that the population mean is less than 64.5.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:### Hypothesis Testing Example
**Objective:** Test the following null hypothesis \( (H_0) \) at a significance level of \( \alpha = 0.005 \).
#### Hypotheses:
- \( H_0: \mu = 64.5 \)
- \( H_a: \mu < 64.5 \)
You believe the population is normally distributed and you know the standard deviation is \( \sigma = 14.9 \). You obtain a sample mean \( M = 62 \) for a sample of size \( n = 28 \).
1. **Determine the Critical Value:**
- Find the critical value for this test.
- **Critical value** box: (Enter answer accurate to three decimal places)
2. **Calculate the Test Statistic:**
- Determine the test statistic for this sample.
- **Test statistic** box: (Enter answer accurate to three decimal places)
3. **Decision on the Test Statistic:**
- Evaluate if the test statistic is:
- \( \circ \) in the critical region
- \( \circ \) not in the critical region
4. **Conclusion from the Test Statistic:**
- Make a decision based on the test statistic:
- \( \circ \) reject the null
- \( \circ \) accept the null
- \( \circ \) fail to reject the null
5. **Final Conclusion:**
- Determine the final conclusion of the test:
- \( \circ \) There is sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5.
- \( \circ \) There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 64.5.
- \( \circ \) The sample data support the claim that the population mean is less than 64.5.
- \( \circ \) There is not sufficient sample evidence to support the claim that the population mean is less than 64.5.
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