题目
Problem
A manager claims that the lengths of the rubber tubes that his company produces have a median of 5.50 cm. The lengths, in cm, of a random sample of 11 tubes produced by this company are as follows.
It is required to test at the 10% significance level the null hypothesis that the population median length is 5.50 cm against the alternative hypothesis that the population median length is not equal to 5.50 cm.
Show that both a sign test and a Wilcoxon signed-rank test give the same conclusion and state this conclusion.
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题目中文翻译
一名经理声称，他的公司生产的橡胶管长度的中位数为 5.50 cm。该公司生产的 11 根橡胶管组成一个随机样本，其长度（单位 cm）如下。
要求在 10% 显著性水平下，检验总体长度中位数为 5.50 cm 的原假设，对立假设为总体长度中位数不等于 5.50 cm。
证明符号检验和 Wilcoxon 符号秩检验会给出相同结论，并说明该结论。