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
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.
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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