### Testing Hypothesis for Standard Deviations#### Problem Overview:Test the hypothesis that σ1 < σ2 at the α = 0.05 level of significance for the given sample data. Assume that the populations are normally distributed. Use the P-value approach.#### Sample Data:| | Population 1 | Population 2 ||------------------|--------------|--------------|| **n** | 52 | 25 || **s** | 8.3 | 11.9 |#### Hypothesis Statements:State the null and alternative hypotheses for this test.- **H0 (Null Hypothesis)** should be stated using "≥": $ H_0: \sigma_1 \geq \sigma_2 $- **H1 (Alternative Hypothesis)** should be stated using "<": $ H_1: \sigma_1 < \sigma_2 $#### P-Value Calculation:Use technology to find the P-value for this test.- **The P-value is** [ Empty Box ].- (Round to three decimal places as needed.)#### Conclusion:Make a statement regarding the null hypothesis and draw a conclusion for this test.1. **Since the P-value is** [ Drop-down Box ] **the α = 0.05 level of significance**, - **Option to accept/reject the null hypothesis**: [ Drop-down Box to choose "reject" or "do not reject" ]2. **Sufficient evidence statement**: - "There [ Drop-down Box: "is" or "is not"] sufficient evidence to conclude that the standard deviation of Population 1 is significantly less than the standard deviation of Population 2 at the α = 0.05 level of significance."---### Graphs or Diagrams:The image does not contain any graphs or diagrams. The problem focuses on hypothesis testing for comparing the standard deviations of two populations using the P-value approach, given certain sample data. This explanation and format can help students understand and work step-by-step through the process of hypothesis testing for standard deviation comparisons.

Answered: Test the hypothesis that o,

Math

Statistics

Test the hypothesis that o,

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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Question

### Testing Hypothesis for Standard Deviations

#### Problem Overview:
Test the hypothesis that σ1 < σ2 at the α = 0.05 level of significance for the given sample data. Assume that the populations are normally distributed. Use the P-value approach.

#### Sample Data:

| | Population 1 | Population 2 |
|------------------|--------------|--------------|
| **n** | 52 | 25 |
| **s** | 8.3 | 11.9 |

#### Hypothesis Statements:
State the null and alternative hypotheses for this test.
- **H0 (Null Hypothesis)** should be stated using "≥":
$ H_0: \sigma_1 \geq \sigma_2 $
- **H1 (Alternative Hypothesis)** should be stated using "<":
$ H_1: \sigma_1 < \sigma_2 $

#### P-Value Calculation:
Use technology to find the P-value for this test.

- **The P-value is** [ Empty Box ].
- (Round to three decimal places as needed.)

#### Conclusion:
Make a statement regarding the null hypothesis and draw a conclusion for this test.
1. **Since the P-value is** [ Drop-down Box ] **the α = 0.05 level of significance**,
- **Option to accept/reject the null hypothesis**: [ Drop-down Box to choose "reject" or "do not reject" ]
2. **Sufficient evidence statement**:
- "There [ Drop-down Box: "is" or "is not"] sufficient evidence to conclude that the standard deviation of Population 1 is significantly less than the standard deviation of Population 2 at the α = 0.05 level of significance."

---

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The image does not contain any graphs or diagrams. The problem focuses on hypothesis testing for comparing the standard deviations of two populations using the P-value approach, given certain sample data.

This explanation and format can help students understand and work step-by-step through the process of hypothesis testing for standard deviation comparisons.

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