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。
- (i)
解释如何进行系统抽样。
- (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。
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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 sample is required, the sampling interval is .
2. Explain the random starting point and the systematic selection of subsequent units.
Randomly select a starting number between and inclusive. Select the household numbered , and then select every th household thereafter (i.e., households numbered ) until of the households are chosen.
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).
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.
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