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A coin is tossed 20 times and lands heads 16 times…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A coin is tossed times and lands heads times. A referee asks whether the coin is unfair in either direction, so the test is two-sided. Find the one-sided p-value for a fair coin, to five decimal places. Find the two-sided p-value. Decide at the level, and at the level.
Need a reminder? The key ideaShow
The null idea says nothing special is going on, and the alternative is what we suspect. The p-value is the chance, if the null idea were true, of a result at least as extreme as the one seen.
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. Count. .
Step 2. One side. .
Step 3. Two sides. .
Step 4. Decide. , so reject the null idea at the level. , so do not reject it at the level.
Answer: and . Significant at , not at .
Watch out. Using the one-sided value for a two-sided question would make the result look significant at the level, which it is not.
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