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A player suspects a die of showing too many sixes…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A player suspects a die of showing too many sixes. She rolls it times and gets sixes. Under the null idea, the number of sixes follows the binomial distribution with and . Find the p-value , to four decimal places. Is the result significant at the level? Is it significant 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. The terms. , , , and the rest are tiny.
Step 2. The p-value. Their total is about .
Step 3. The decisions. , so the result is significant at the level. , so it is not significant at the level.
Answer: about : significant at , not at .
What it means. A fair die gives or more sixes in rolls a little less than four times in a hundred. That is some evidence, but not strong evidence.
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