Four siblings (Colin, Rose, Iris, and Lily) are trying to find a way to determin

Question

Four siblings (Colin, Rose, Iris, and Lily) are trying to find a way to determine who does the dishes after dinner every night. The oldest, Colin, suggests that each night they can draw a name out of a bucket which would determine the sibling responsible for the dishes that night.

(a) What is the probability that Colin gets chosen on any given night? What is the probability that he doesn’t?

(b) Ten nights have passed and Colin hasn’t been selected to do the dishes on any of them. Rose starts suspecting that Colin may be cheating, so she decides to do a hypothesis test. What are the null and alternative hypotheses?

(c) Calculate the probability that Colin does not get picked at all on 10 consecutive nights.

(d) Given a threshold of 5%, should Rose stick to the null hypothesis or should she go with the alternative hypothesis?

Explanation / Answer

Four siblings (Colin, Rose, Iris, and Lily) are trying to find a way to determine who does the dishes after dinner every night. The oldest, Colin, suggests that each night they can draw a name out of a bucket which would determine the sibling responsible for the dishes that night.

(a) What is the probability that Colin gets chosen on any given night? What is the probability that he doesn’t?

(b) Ten nights have passed and Colin hasn’t been selected to do the dishes on any of them. Rose starts suspecting that Colin may be cheating, so she decides to do a hypothesis test. What are the null and alternative hypotheses?

(c) Calculate the probability that Colin does not get picked at all on 10 consecutive nights.

(d) Given a threshold of 5%, should Rose stick to the null hypothesis or should she go with the alternative hypothesis?

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