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A games club suspects that one of its dice shows a six too often…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A games club suspects that one of its dice shows a six too often. A member plans to roll it times and count the sixes. Write the null idea and the alternative idea, using for the chance of a six. Find the number of sixes expected under the null idea. Say whether a result of sixes would be evidence against the null idea.
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 ideas. : , the die is fair. : , the die shows a six too often.
Step 2. Expected. sixes.
Step 3. The result. sixes is just one more than expected. A fair die often does that.
Answer: sixes expected. A result of is not evidence against the fair die.
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