A random sample of size 15 is drawn from a continuous and symmetric probability distribution with mean $\mu .$ In testing $H _ { o } : \mu = 300 \text { versus } H _ { a } : \mu \neq 300$ using the Wilcoxon signed-rank test with approximate level of significance of .05, the rejection region for the test is
A) $s _ { + } \geq 95$
B) $s _ { + } \leq 25$
C) either $s _ { + } \geq 95$
Or $s _ { + } \leq 25$
D) $s _ { + } \leq 95$
E) $s _ { + } \geq 25$

Question

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a non-parametric test used to compare the median of a single sample to a specified value (in this case, $\mu = 300$) or to compare the medians of two related samples. For a two-tailed test (as indicated by $H_a: \mu \neq 300$), the rejection region is at both ends of the distribution of the test statistic. Therefore, the correct answer involves rejecting the null hypothesis for extreme values of the test statistic, both high and low, which is represented by option C: either $s _ { + } \geq 95$ or $s _ { + } \leq 25$. This captures the essence of a two-tailed test where extreme values in either direction are evidence against the null hypothesis.

A Random Sample of Size 15 Is Drawn from a Continuous