HardStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Learning from SamplesNumericalapplication
A charity runs a pilot survey of 200 households, chosen at random, and 60 of them say they would…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A charity runs a pilot survey of households, chosen at random, and of them say they would give to a new appeal. Find the margin of error of the pilot's 95% interval, to four decimal places. The charity wants a margin of at most in the full survey. Using the pilot's share as the guess, how many households must the full survey ask? How many times as large as the pilot is that?
Need a reminder? The key ideaShow
The interval for a proportion is . It needs a random sample with at least successes and failures. For a margin , .
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 pilot. .
Step 2. The full survey. , so households.
Step 3. Compare. .
Answer: , households and times.
Check. The margin falls from about to , a factor of about . The square of is about , which matches.
Discussion (0)
Log in to join the discussion.
Loading…