Suppose a coin with probability p of heads is repeatedly flipped until 10 heads appear.

kokoszzm

kokoszzm

Answered question

2022-06-22

Suppose a coin with probability p of heads is repeatedly flipped until 10 heads appear. Call this number X. Find the p-value of H 0 : p = 0.5 versus the alternate H a : p 0.5 using the test statistic | X 20 | if X = 27.

Answer & Explanation

Cristian Hamilton

Cristian Hamilton

Beginner2022-06-23Added 23 answers

The p-values is the probability that you observe something at least as crazy as what happened if you assume H 0 . In this case, X is 27, so you need to calculate P [ | X 20 | 7 | p = 0.5 ]. You need to use the negative binomial distribution to calculate this number. If it's smaller than your cutoff ( 0.05 is a standard cutoff), you would reject the null. Otherwise, you accept that you don't have enough information to reject the null.

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