F statistic comparing two bolt variances

Question

Twelve bolts from one manufacturer have a sample variance in diameter of $0.0003$ ; twelve bolts from a rival have a sample variance of $0.0001$ . You want to know whether the rival's bolts vary less. Assuming independent samples and normally distributed diameters, what is the value of the appropriate test statistic?

Short answer

$F=3$ . Comparing two normal variances uses the F-test, with the larger sample variance on top: $F=0.0003/0.0001=3$ , referred to an $F_{11,11}$ distribution.

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Lessons behind this question

The Hypothesis Testing Framework
Independence
Covariance and Correlation

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