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:

  1. ((i))

    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。

  2. ((ii))

    说明(i)中所建议抽样方法的一个优点和一个缺点。

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完整解法

5((i))

1. Identify the appropriate sampling method and calculate the number of participants to sample from each stratum.

The appropriate method is stratified sampling, as the population is divided into distinct subgroups.
The proportion of the population to be sampled is 80800=110\frac{80}{800} = \frac{1}{10}.
The number of participants to select from each educational institution is:

  • Primary school: 350×110=35350 \times \frac{1}{10} = 35
  • Secondary school: 250×110=25250 \times \frac{1}{10} = 25
  • Junior college: 150×110=15150 \times \frac{1}{10} = 15
  • Polytechnic: 50×110=550 \times \frac{1}{10} = 5

2. Describe the random selection process within each stratum.

Within each of the 4 educational institution groups, assign a unique index to each participant. Then, use a random number generator to independently select the calculated number of unique participants from each group (i.e. by simple random sampling).

答案

Use stratified sampling. Select 35 participants from Primary school, 25 from Secondary school, 15 from Junior college, and 5 from Polytechnic. Within each group, select the participants independently using simple random sampling (e.g., using a random number generator).

5((ii))

1. State an advantage of stratified sampling

Advantage: It ensures that the sample is representative of the population by maintaining the proportion of participants from each educational institution.

2. State a disadvantage of stratified sampling

Disadvantage: It is time-consuming and administrative-heavy, as it requires the population to be divided into distinct strata and a separate sampling frame to be compiled for each subgroup before randomly selecting from them.

答案

Advantage: The sample is highly representative of the population as it ensures that the proportion of participants from each educational institution matches that in the population.

Disadvantage: It requires more administrative effort and is more time-consuming, as a complete sampling frame is needed for each distinct educational institution subgroup.

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