过去，某种植物的平均高度为 $2.3\,\mathrm{m}$。随机抽取该种植物 $60$ 株，施用肥料，测得这 $60$ 株植物的平均高度为 $2.4\,\mathrm{m}$。假设施肥后植物高度的标准差为 $0.4\,\mathrm{m}$。

在 $2.5\%$ 的显著性水平下检验施肥后的植物平均高度是否大于 $2.3\,\mathrm{m}$。

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。

以施肥后总体平均高度为参数作右尾检验，使用已知标准差0.4及60的样本量。

Let $\mu$ be the population mean height of plants treated with fertiliser, in metres.

Using the large-sample normal approximation,

The upper-tail 2.5% critical value is $1.96$. Since $1.93649\ldots<1.96$, we do not reject $H_0$.

There is insufficient evidence at the 2.5% significance level that the population mean height of treated plants is greater than 2.3 m.