Use the information provided to answer the questions. Population 2 Sample Size 15 13 Sample Mean 34.9 32.3 Sample Variance 4.6 5.6 n USE SALT State the null and alternative hypotheses for testing for a significant difference in means. O H;: (u, - 4,) = 0 versus H.: (4, - H,) > 0 O Ho: (H, - H2) = 0 versus H: (u, - u2) < 0 O H,: (4, - 42) = 0 versus H: (u, - 42) # 0 O H: (H, - H2) < 0 versus H.: (4, - H2) > 0 O Ho: (u, - u2) # 0 versus H: (u, - 42) = 0 Calculate the pooled estimate of o?, the associated degrees of freedom, and the observed value of the t statistic. (Round s? and your t statistic to three decimal places. s2 = df = t = What is the rejection region using a = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t>
Use the information provided to answer the questions. Population 2 Sample Size 15 13 Sample Mean 34.9 32.3 Sample Variance 4.6 5.6 n USE SALT State the null and alternative hypotheses for testing for a significant difference in means. O H;: (u, - 4,) = 0 versus H.: (4, - H,) > 0 O Ho: (H, - H2) = 0 versus H: (u, - u2) < 0 O H,: (4, - 42) = 0 versus H: (u, - 42) # 0 O H: (H, - H2) < 0 versus H.: (4, - H2) > 0 O Ho: (u, - u2) # 0 versus H: (u, - 42) = 0 Calculate the pooled estimate of o?, the associated degrees of freedom, and the observed value of the t statistic. (Round s? and your t statistic to three decimal places. s2 = df = t = What is the rejection region using a = 0.05? (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t>
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
3
![**Statistics and Hypothesis Testing: An Example**
This is an exercise on how to use statistical data to test for significant differences in means between two populations. Below are the key steps and calculations involved.
**Given Data:**
- **Population 1:**
- Sample Size: 15
- Sample Mean: 34.9
- Sample Variance: 4.6
- **Population 2:**
- Sample Size: 13
- Sample Mean: 32.3
- Sample Variance: 5.6
**Hypothesis Testing:**
1. **State the Null and Alternative Hypotheses:**
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) > 0\)
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) < 0\)
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) \neq 0\)
2. **Calculate Pooled Estimate of Variance (\(s^2\)), Degrees of Freedom (df), and t Statistic (t):**
- Use the formula for pooled variance and t-statistics as required, rounded to three decimal places.
3. **Determine the Rejection Region (\(\alpha = 0.05\)):**
- Depending on whether the test is one-tailed or two-tailed, fill in the appropriate rejection region boundary values.
4. **Evaluate the p-value for the Test:**
- Choose the appropriate interval for p-value.
5. **Conclusion From Data:**
- State whether \(H_0\) is rejected or not, based on the p-value and test results.
- Draw a conclusion on whether there is sufficient evidence to declare a significant difference between the population means.
This exercise helps in applying statistical concepts to real-world problems by performing hypothesis testing, understanding variance, degrees of freedom, and calculating the significance of results using the p-value approach.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0043636e-317e-482a-b701-46e9ae6bab2e%2F18a7af81-6576-411e-bcea-8be67c26bbc4%2Fn3flsuk_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistics and Hypothesis Testing: An Example**
This is an exercise on how to use statistical data to test for significant differences in means between two populations. Below are the key steps and calculations involved.
**Given Data:**
- **Population 1:**
- Sample Size: 15
- Sample Mean: 34.9
- Sample Variance: 4.6
- **Population 2:**
- Sample Size: 13
- Sample Mean: 32.3
- Sample Variance: 5.6
**Hypothesis Testing:**
1. **State the Null and Alternative Hypotheses:**
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) > 0\)
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) < 0\)
- \(H_0: (\mu_1 - \mu_2) = 0\) versus \(H_a: (\mu_1 - \mu_2) \neq 0\)
2. **Calculate Pooled Estimate of Variance (\(s^2\)), Degrees of Freedom (df), and t Statistic (t):**
- Use the formula for pooled variance and t-statistics as required, rounded to three decimal places.
3. **Determine the Rejection Region (\(\alpha = 0.05\)):**
- Depending on whether the test is one-tailed or two-tailed, fill in the appropriate rejection region boundary values.
4. **Evaluate the p-value for the Test:**
- Choose the appropriate interval for p-value.
5. **Conclusion From Data:**
- State whether \(H_0\) is rejected or not, based on the p-value and test results.
- Draw a conclusion on whether there is sufficient evidence to declare a significant difference between the population means.
This exercise helps in applying statistical concepts to real-world problems by performing hypothesis testing, understanding variance, degrees of freedom, and calculating the significance of results using the p-value approach.
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