The Ministry of Urban Development wishes to find out how the recent property cooling measures have affected Singaporeans. A survey is to be carried out on 5% of the households in a particular constituency.

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

1. Obtain a complete numbered list (sampling frame) of all households in the constituency.
2. Randomly select a starting integer, $r$, between 1 and 20 inclusive.
3. 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.

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).