城市发展部希望了解最近的房地产降温措施对新加坡人产生了怎样的影响。计划对某一选区中 5% 的住户进行调查。

(i)
解释如何进行系统抽样。
(ii)
描述在这种情况下一项更好的替代抽样方法。

总体与简单随机样本 English

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完整解法

6(i)

1. Determine the sampling interval

A $5\%$ sample means selecting $\frac{5}{100} = \frac{1}{20}$ of the population.
Thus, the sampling interval is $20$ .

2. Describe the systematic selection process

Obtain a complete numbered list (sampling frame) of all households in the constituency.
Randomly select a starting integer, $r$ , between 1 and 20 inclusive.
Select the $r$ -th household, and then select every 20th household on the list (i.e., households numbered $r+20, r+40, r+60, \dots$ ) to be surveyed.

答案

Obtain a complete numbered list of all households in the constituency. Since a 5% sample is required ( $5\% = \frac{1}{20}$ ), select a random starting household from the 1st to the 20th household. Thereafter, survey every 20th household on the list.

6(ii)

1. Name the alternative method and explain how to group the population based on the specific context.

Stratified sampling. Divide the households in the constituency into distinct strata based on housing types (e.g., HDB flats, condominiums, landed properties).

2. Explain how to randomly sample within the groups.

Select a simple random sample of households from each stratum such that the number of households sampled from each stratum is proportional to the total number of households in that stratum (i.e., selecting 5% from each stratum).

答案

Stratified sampling. Divide the households in the constituency into strata based on housing types (e.g. HDB, condominium, landed). Take a simple random sample from each stratum such that the number of households sampled from each stratum is proportional to the total number of households in that stratum.

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城市发展部希望了解最近的房地产降温措施对新加坡人产生了怎样的影响。计划对某一选区中 5% 的住户进行调查。

完整解法

6(i)

6(ii)

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