螺栓方差

Bolt Variance

专题: Statistics / 统计
难度: L2
来源: OpenQuant

题目详情

某制造商生产螺母和螺栓。随机抽取 12 个该制造商的螺栓，得到样本方差为 .0003；又从竞争对手处随机抽取 12 个螺栓，得到样本方差为 .0001。我们希望检验是否有足够证据表明竞争对手的螺栓直径波动更小。相关检验统计量的值是多少？假设样本独立、方差齐性，且直径方差近似服从正态分布。

A manufacturer produces nuts and bolts. A random sample of twelve bolts returned a sample variance of .0003, while a random sample of twelve bolts from a competitor returned a sample variance of .0001. We wish to test if there is sufficient data to indicate a smaller variation in bolt diameter from the competitor. What is the value of the relevant test statistic? Assume independence, variance homogeneity, and that diameter variance is approximately normally distributed.

解析

要检验是否有足够证据表明竞争对手的螺栓直径方差更小，我们使用方差的 F 检验。F 检验统计量为：

F = \frac{s_1^2}{s_2^2} = \frac{0.0003}{0.0001} = \boxed{3}

Original Explanation

To test whether there is sufficient evidence to indicate a smaller variation in bolt diameter from the competitor, we use an F-test for variances. The test statistic for the F-test is given by:

F = \frac{s_1^2}{s_2^2} = \frac{0.0003}{0.0001} = \boxed{3}