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A made-up factory claims that 10% of its light bulbs fail a strength test…
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 factory claims that of its light bulbs fail a strength test. An inspector tests bulbs, and of them fail. Find the share that failed. If the claim were true, the share would land within a band around in about runs out of . Find the half-width of the band and its two ends. Does the test fit the claim?
Need a reminder? The key ideaShow
In about runs out of , the share of successes in tries lands within of the probability . For a fair coin this is .
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 share. .
Step 2. The band. . So the band is from to .
Step 3. Compare. is outside the band. A share this high would be rare if only of the bulbs failed.
Answer: ; half-width ; band to . The test does not fit the claim well. More bulbs seem to fail.
Watch out. This does not prove that the claim is false. A rare result can still happen. The last chapter of this book turns this idea into a proper test.
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