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.
  1. (i)

    Explain how a systematic sample might be carried out.

  2. (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 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.

Answer

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).

Answer

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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