一名研究者认为某总体的中位数 $m$ 已经从其已知的先前值 $m_0$ 发生了改变。该研究者收集了一个容量为 28 的随机样本。她对数据进行排序，并使用 Wilcoxon 符号秩检验计算检验统计量 $T$。在 1% 显著性水平下进行检验后的结论是，没有足够证据支持她的看法。

使用正态近似，求 $T$ 的最小可能值。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

备择假设是中位数发生变化，所以显著性水平平分到两尾。较小秩和的临界点用下尾，并加 $0.5$ 作连续性修正。

Under the null hypothesis, the sum of the positive ranks has mean and variance

The test statistic $T$ is the smaller of the positive and negative rank sums. By symmetry, a lower-tail probability for one signed sum is compared with $0.005$ for this two-sided test. To be outside the rejection region, the corrected statistic must satisfy

This gives $T>89.375\ldots$. Since $T$ is an integer, the least possible value is $90$.