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A made-up district has 8000 households: 5000 in the town and 3000 in the villages…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up district has 8000 households: 5000 in the town and 3000 in the villages. A survey takes a random sample of 40 households from the town and another of 40 from the villages. The town sample has a mean of people per household, and the village sample a mean of . Estimate the mean household size of the whole district by weighting each stratum. A clerk simply averages the two sample means instead. Find the clerk's answer, and by how much it overstates the weighted estimate.
Need a reminder? The key ideaShow
Systematic: step and a random start. Stratified: a simple random sample inside each stratum; proportional allocation gives stratum the share . Cluster: whole groups chosen at random. An estimate from strata weights each stratum by its share of the population.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The weights. Town: . Villages: .
Step 2. The weighted estimate. people.
Step 3. The clerk. people. This treats the two strata as if they were the same size.
Step 4. The gap. people.
Answer: people per household. The clerk's overstates it by people.
Watch out. Equal samples from unequal strata are fine, and they help the smaller stratum. The estimate must then weight each stratum by its real size.
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