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In a made-up town, 40% of the adults are members of a gym…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a made-up town, 40% of the adults are members of a gym. Of the members, 90% exercise at least once a week. Of the other adults, 35% do. A health team stands at the gym door and asks people whether they exercise at least once a week. Find the true percentage for the whole town, the percentage the survey is likely to find, and the bias in percentage points.
Need a reminder? The key ideaShow
Bias is a slant in the way a sample is chosen. If of a population are easy to reach and the survey asks only them, it finds their view , while the truth is . The gap is the bias, in percentage points.
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 truth. In every 100 adults, members and others exercise weekly. So the truth is .
Step 2. The survey. It asks members only, so it finds about .
Step 3. The bias. percentage points.
Answer: , and percentage points.
Check. The truth must lie between the two groups, and , and nearer the larger group of non-members. does.
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