B 组:统计 [60 分]

某住宅小区的镇理事会希望了解该小区居民是否希望建设一个菜市场。将对该小区 10% 的住户进行调查。
  1. (i)

    解释如何进行系统抽样。

  2. (ii)

    描述另一种可采用的抽样方法,并说明该方法相比系统抽样的一个优点。

先不看答案,让 AI 诊断你卡在哪里?

它不会直接告诉你答案,而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

6(i)

1. State the preparation of the sampling frame and calculate the sampling interval.

Obtain a list of all the households in the housing estate and number them sequentially. Since a 10%10\% sample is required, the sampling interval is k=10010=10k = \frac{100}{10} = 10.

2. Explain the random starting point and the systematic selection of subsequent units.

Randomly select a starting number rr between 11 and 1010 inclusive. Select the household numbered rr, and then select every 1010th household thereafter (i.e., households numbered r+10,r+20,…r+10, r+20, \dots) until 10%10\% of the households are chosen.

答案

Obtain a numbered list of all the households in the housing estate. Randomly select a starting household from the first 10 households on the list. Thereafter, select every 10th household on the list until 10% of the households are chosen.

6(ii)

1. Describe an alternative method of sampling that fits the context.

Method: Stratified Sampling
Divide the households in the estate into mutually exclusive strata based on their flat type (e.g., 3-room, 4-room, 5-room). Within each stratum, randomly select 10% of the households using simple random sampling to form the final sample.

(Note: Simple Random Sampling is also an acceptable alternative method.)

2. State one advantage of this method over systematic sampling.

Advantage:
Stratified sampling ensures that every flat type (and thus demographic group) is proportionally represented in the sample. Systematic sampling might under-represent or over-represent certain flat types, especially if the sampling interval coincides with a periodic, structural pattern in the list of households (e.g., always picking corner units).

答案

Method: Stratified Sampling
Divide the households into strata based on flat type (e.g., 3-room, 4-room, 5-room). Within each stratum, randomly select 10% of the households using simple random sampling.

Advantage over systematic sampling:
It ensures that the sample is proportionally representative of all flat types in the housing estate. Systematic sampling might under-represent or over-represent a specific flat type by chance or if there is a periodic pattern in the sampling frame.

AI 分析,可能出错

用 AI 批改,圈出写错的那一步,并自动将你的薄弱点存入错题本,形成你的错因库。

同一知识点的其他题

  1. 1会议组织者希望对 80 名参会者进行调查,以收集他们对会议体验的反馈。参加会议的 800 名参会者来自不同的教育机构,如下表所示: 简要描述如何使用适当的抽样方法抽取 80 名参会者的样本。 说明(i)中所建议抽样方法的一个优点和一个缺点。
  2. 2第二部分:统计 [60分] 某公司有 1500 名员工。35% 的员工处于 21-40 岁年龄段,50% 处于 41-60 岁年龄段,其余处于 60 岁及以上年龄段。 将抽取一个包含 50 名员工的样本来参与一项关于员工士气的调查。生成一份…
  3. 3一家公司由 150 名程序员、15 名秘书和 15 名部门主管组成。公司老板想要收集整个公司的反馈。请在此背景下说明,如何使用分层抽样抽取一个容量为 12 的样本,并指出分层抽样的一个优点。
  4. 4B部分:统计学 [60分] 一家公司想要了解其员工的通勤习惯。在某个特定的工作日,调查员通过以下方式从进入公司大楼的员工中抽取样本进行访谈: - 站在大楼入口处,随机选择前10名进入大楼的员工中的一人, - 然后在选定第一名员工后,每隔10…
  5. 5在一个拥有 1000 名会员的社交俱乐部中,执行委员会希望调查会员对俱乐部所组织活动的意见。 给出委员会宁愿获取意见样本而不询问所有会员的一个可能原因。 解释如何获取一个容量为 100 的系统样本。 给出在此背景下使用系统抽样的一个缺点。…