### 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...
Related questions
Question
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON