Heat the claim about the difference between two population means p, and ₂ at the level of significance a Assume the samples are random and independent, and the populations are normally distributed Clam pa=0.01 Population parameters, 33, ₂15 Sample statistics x,-18, n, 27, X=20, n₂ = 26 Determine the alternative hypothesis Determine the standardized test statstic z=(Round to two decimal places as needed) Determine the P-value. P-value- (Round to three decimal places as needed) What is the proper decision? OA Fal to reject H, There is not enough evidence at the 1% level of significance to reject the claim OB Reject H, There is not enough evidence at the 1% level of significance to reject the claim OC. Fal to reject H, There is enough evidence at the 1% level of significance to reject the claim OD. Rejed H, There is enough evidence at the 1% level of significance to reject the clam
Heat the claim about the difference between two population means p, and ₂ at the level of significance a Assume the samples are random and independent, and the populations are normally distributed Clam pa=0.01 Population parameters, 33, ₂15 Sample statistics x,-18, n, 27, X=20, n₂ = 26 Determine the alternative hypothesis Determine the standardized test statstic z=(Round to two decimal places as needed) Determine the P-value. P-value- (Round to three decimal places as needed) What is the proper decision? OA Fal to reject H, There is not enough evidence at the 1% level of significance to reject the claim OB Reject H, There is not enough evidence at the 1% level of significance to reject the claim OC. Fal to reject H, There is enough evidence at the 1% level of significance to reject the claim OD. Rejed H, There is enough evidence at the 1% level of significance to reject the clam
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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![### Testing the Difference Between Two Population Means
**Objective:** Test the claim about the difference between two population means \( \mu_1 \) and \( \mu_2 \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed.
#### Given Data:
- **Claim:** \( H_1: \mu_1 \ne \mu_2 \)
- **Significance Level:** \( \alpha = 0.01 \)
- **Population Parameters:**
- Standard Deviation of Population 1 (\( \sigma_1 \)) = 3.3
- Standard Deviation of Population 2 (\( \sigma_2 \)) = 1.5
- **Sample Statistics:**
- Sample Mean of Group 1 (\( \bar{x}_1 \)) = 11
- Sample Size of Group 1 (\( n_1 \)) = 27
- Sample Mean of Group 2 (\( \bar{x}_2 \)) = 20
- Sample Size of Group 2 (\( n_2 \)) = 26
### Steps for Hypothesis Testing
1. **Determine the Alternative Hypothesis:**
\[
H_1: \mu_1 \ne \mu_2
\]
2. **Determine the Standardized Test Statistic:**
Use the formula for the Z-test statistic for difference between two means:
\[
z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\left(\frac{\sigma_1^2}{n_1}\right) + \left(\frac{\sigma_2^2}{n_2}\right)}}
\]
Substituting the given values:
\[
z = \frac{(11 - 20)}{\sqrt{\left(\frac{3.3^2}{27}\right) + \left(\frac{1.5^2}{26}\right)}}
\]
Perform the calculations:
\[
z = \frac{-9}{\sqrt{\left(\frac{10.89}{27}\right) + \left(\frac{2.25}{26}\right)}} \approx \frac{-9}{\sqrt{0.4033 + 0.0865}} \approx \frac{-9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5386f0c-0c7d-4f0c-9c77-b0195c82b8c2%2Fca5eaf38-1cde-485a-a0d7-331733142897%2F1bte4v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Testing the Difference Between Two Population Means
**Objective:** Test the claim about the difference between two population means \( \mu_1 \) and \( \mu_2 \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed.
#### Given Data:
- **Claim:** \( H_1: \mu_1 \ne \mu_2 \)
- **Significance Level:** \( \alpha = 0.01 \)
- **Population Parameters:**
- Standard Deviation of Population 1 (\( \sigma_1 \)) = 3.3
- Standard Deviation of Population 2 (\( \sigma_2 \)) = 1.5
- **Sample Statistics:**
- Sample Mean of Group 1 (\( \bar{x}_1 \)) = 11
- Sample Size of Group 1 (\( n_1 \)) = 27
- Sample Mean of Group 2 (\( \bar{x}_2 \)) = 20
- Sample Size of Group 2 (\( n_2 \)) = 26
### Steps for Hypothesis Testing
1. **Determine the Alternative Hypothesis:**
\[
H_1: \mu_1 \ne \mu_2
\]
2. **Determine the Standardized Test Statistic:**
Use the formula for the Z-test statistic for difference between two means:
\[
z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\left(\frac{\sigma_1^2}{n_1}\right) + \left(\frac{\sigma_2^2}{n_2}\right)}}
\]
Substituting the given values:
\[
z = \frac{(11 - 20)}{\sqrt{\left(\frac{3.3^2}{27}\right) + \left(\frac{1.5^2}{26}\right)}}
\]
Perform the calculations:
\[
z = \frac{-9}{\sqrt{\left(\frac{10.89}{27}\right) + \left(\frac{2.25}{26}\right)}} \approx \frac{-9}{\sqrt{0.4033 + 0.0865}} \approx \frac{-9
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