
MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Hypothesis Testing Using P-Value Approach**
**Objective:**
Test the hypothesis that the population standard deviations \( \sigma_1 \neq \sigma_2 \) at the \( \alpha = 0.01 \) level of significance for the given sample data. Assume that the populations are normally distributed.
**Data:**
- **Population 1:**
- Sample size (\( n \)): 19
- Sample standard deviation (\( s \)): 3.1
- **Population 2:**
- Sample size (\( n \)): 19
- Sample standard deviation (\( s \)): 4.8
**Instructions:**
1. **State the Hypotheses:**
- **Null Hypothesis (\( H_0 \)):** \( \sigma_1 = \sigma_2 \)
- **Alternative Hypothesis (\( H_1 \)):** \( \sigma_1 \neq \sigma_2 \)
2. **Use the P-value Approach:**
- Calculate the test statistic.
- Determine the p-value.
- Compare the p-value to the significance level (\( \alpha = 0.01 \)).
- Draw conclusions based on the comparison.
**Note:** Ensure data is normally distributed to correctly apply the test.
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