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A researcher takes a random sample of 400 adults, without replacement, in a made-up town of 5000…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A researcher takes a random sample of adults, without replacement, in a made-up town of adults, where the true share who own a bicycle is . A colleague takes a random sample of in a country of million adults with the same true share. When the sample is a large part of the population, the standard error is multiplied by a correction factor , where is the population size. Find the standard error from the formula . Find the correction factor for the town. Find the corrected standard error for the town. Find the correction factor for the country. Give all answers to four decimal places.
Need a reminder? The key idea
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 formula. .
Step 2. The town. .
Step 3. Corrected. .
Step 4. The country. , which is to four places.
Answer: , , and .
What it means. Even in the town, where the sample is of the adults, the correction is only about . In the country it is nothing. The sample size, not the population size, sets the precision.
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