
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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system
From four independent samples of the same size \( n = 17 \), drawn from normal populations, the corrected sample variances found are: \( 0.21 \), \( 0.25 \), \( 0.34 \), \( 0.40 \).

Required: 
a) At a significance level of 0.05, test the null hypothesis of the homogeneity of variances (the critical region is right-sided).
b) Estimate the population variance.

Present the answer in LaTex format: \boxed{Your answer}
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