Section B: Statistics [60 marks]
The town council of a particular housing estate wishes to find out whether the residents of the housing estate want to have a wet market built. A survey is to be carried out on 10% of the households in the housing estate.
- (i)
Explain how a systematic sample might be carried out.
- (ii)
Describe one other method of sampling that could be used, and state one advantage that this method has over systematic sampling.
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Worked solution
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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