State the null and alternative hypotheses used to test for a difference in the two population means. O Ho: (H, - H2) = 0 versus H,: (Hq - H2) < 0 O Ho: (H, - H2) < o versus H,: (Hy - H2) > 0 O Ho: (H, - H2) = 0 versus H,: (H - H2) # 0 O Ho: (H, - H2) = 0 versus H,: (Hq - H2) > 0 O Ho: (H, - H2) * 0 versus H,: (Hq – H2) = 0 Calculate the necessary test statistic. (Round your answer to two decimal places.) z = Calculate the rejection region with a = 0.01. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) Draw the appropriate conclusion.
State the null and alternative hypotheses used to test for a difference in the two population means. O Ho: (H, - H2) = 0 versus H,: (Hq - H2) < 0 O Ho: (H, - H2) < o versus H,: (Hy - H2) > 0 O Ho: (H, - H2) = 0 versus H,: (H - H2) # 0 O Ho: (H, - H2) = 0 versus H,: (Hq - H2) > 0 O Ho: (H, - H2) * 0 versus H,: (Hq – H2) = 0 Calculate the necessary test statistic. (Round your answer to two decimal places.) z = Calculate the rejection region with a = 0.01. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) Draw the appropriate conclusion.
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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![**Independent Random Samples from Two Quantitative Populations**
**Sample Data**
| | Population 1 | Population 2 |
|-----------------|--------------|--------------|
| Sample Size | 32 | 41 |
| Sample Mean | 9.8 | 7.5 |
| Sample Variance | 10.73 | 16.39 |
**Hypothesis Testing for Differences in Population Means**
State the null and alternative hypotheses:
1. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \)
2. \( H_0: (\mu_1 - \mu_2) < 0 \) versus \( H_a: (\mu_1 - \mu_2) \geq 0 \)
3. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \)
4. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \)
5. \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \)
**Test Statistic Calculation**
Calculate the test statistic (z-value), rounded to two decimal places:
\[ z = \text{______} \]
**Rejection Region Calculation**
Calculate the rejection region with \( \alpha = 0.01 \):
- \( z \geq \text{______} \)
- \( z < \text{______} \)
**Conclusion**
Draw the appropriate conclusion based on the hypothesis test:
- \( H_0 \) is rejected. There is sufficient evidence to indicate a difference in mean.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate a difference in mean.
- \( H_0 \) is not rejected. There is sufficient evidence to indicate a difference in mean.
- \( H_0 \) is rejected. There is insufficient evidence to indicate a difference in mean.
This exercise outlines the process of setting up and performing a hypothesis test for differences between](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7104469d-fb7e-48cd-bb9c-a2d8cb607855%2F1c83b0c3-76e9-499e-80b1-55970dba9ab5%2F3v21ji9_processed.png&w=3840&q=75)
Transcribed Image Text:**Independent Random Samples from Two Quantitative Populations**
**Sample Data**
| | Population 1 | Population 2 |
|-----------------|--------------|--------------|
| Sample Size | 32 | 41 |
| Sample Mean | 9.8 | 7.5 |
| Sample Variance | 10.73 | 16.39 |
**Hypothesis Testing for Differences in Population Means**
State the null and alternative hypotheses:
1. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \)
2. \( H_0: (\mu_1 - \mu_2) < 0 \) versus \( H_a: (\mu_1 - \mu_2) \geq 0 \)
3. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \)
4. \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \)
5. \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \)
**Test Statistic Calculation**
Calculate the test statistic (z-value), rounded to two decimal places:
\[ z = \text{______} \]
**Rejection Region Calculation**
Calculate the rejection region with \( \alpha = 0.01 \):
- \( z \geq \text{______} \)
- \( z < \text{______} \)
**Conclusion**
Draw the appropriate conclusion based on the hypothesis test:
- \( H_0 \) is rejected. There is sufficient evidence to indicate a difference in mean.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate a difference in mean.
- \( H_0 \) is not rejected. There is sufficient evidence to indicate a difference in mean.
- \( H_0 \) is rejected. There is insufficient evidence to indicate a difference in mean.
This exercise outlines the process of setting up and performing a hypothesis test for differences between
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