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F statistic comparing two bolt makers' variability

Question

Twelve bolts from one maker have sample variance 0.00030.0003, and twelve from a rival have sample variance 0.00010.0001 (diameters in cm, assumed normal and independent). The question is whether the rival's diameters vary less. What is the value of the appropriate test statistic?

Short answer

F=3F=3. Comparing two normal variances uses the ratio of sample variances, larger over smaller: 0.0003/0.0001=30.0003/0.0001=3, referred to an F11,11F_{11,11} distribution.

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