Harry 有一个五边形转盘，扇区的颜色分别为蓝色、绿色、红色、黄色和黑色。Harry 认为转盘可能有偏。他计划用下列假设进行假设检验。

Harry 转动转盘 $300$ 次，有 $45$ 次停在蓝色扇区。

用适当的近似方法，在 $5\%$ 的显著性水平下进行 Harry 的检验。

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。

原假设下蓝色次数服从二项分布，用均值60、方差48的正态近似；双尾5%检验比较修正后的z与±1.96。

Let $B$ be the number of blue outcomes. We test

where $p$ is the probability of landing on blue. Under $H_0$, $B\sim\mathrm{B}(300,0.2)$. Since $np=60$ and $n(1-p)=240$ are large, use $Y\sim\mathrm{N}(60,48)$. For the observed lower-tail count of 45, continuity correction gives

The two-tailed 5% critical values are $\pm1.96$. Since $z<-1.96$, we reject $H_0$. There is sufficient evidence at the 5% significance level that the spinner is biased with respect to blue.