镇议会公布了重建镇中心的计划，并询问居民是赞成还是反对。从镇上四条主要街道 North、East、South 和 West Streets 的居民中随机抽取了 250 份回应。结果如下表所示。

在 5% 显著性水平下检验居民意见是否与他们居住的街道相互独立。

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。

在独立假设下，每个期望频数等于行总数乘列总数再除以总样本量。由列联表的尺寸确定自由度。

Let $H_0$ be that opinion on the plan is independent of street and $H_1$ that the two variables are associated. The row totals are $155$ and $95$, and the column totals are $52,93,70,35$. For example, the expected number approving on North Street is $155(52)/250=32.24$. The expected counts are

All exceed $5$. The statistic is

There are $(2-1)(4-1)=3$ degrees of freedom. The upper $5\%$ critical value is $7.815$. Since the statistic is smaller, we fail to reject $H_0$. There is insufficient evidence at the $5\%$ level that residents’ opinions depend on their street.