It is claimed that a vitamin supplement helps mice learn to run a maze more quickly and, in fact, to beat a non-treated mouse 70% of the time (whereas without the supplement, it would only win half of the time). To test this claim, you divide a group of 20 mice randomly into ten pairs, giving one of each pair the vitamin supplement. You run each pair through the maze and find that seven out of ten of the mice treated with the vitamin supplement beat the untreated mice. a) What is the probability of obtaining this result if the claim is true? b) What is the probability of obtaining this result if the claim is false (i.e., the supplement has no effect)? c) Suppose before you ran this experiment, you thought it was equally likely that the claim was true or false. After running the experiment, what is your belief? What is the updated probability?

It is claimed that a vitamin supplement helps mice learn to run a maze more quickly and, in fact, to beat a non-treated mouse 70% of the time (whereas without the supplement, it would only win half of the time). To test this claim, you divide a group of 20 mice randomly into ten pairs, giving one of each pair the vitamin supplement. You run each pair through the maze and find that seven out of ten of the mice treated with the vitamin supplement beat the untreated mice. a) What is the probability of obtaining this result if the claim is true? b) What is the probability of obtaining this result if the claim is false (i.e., the supplement has no effect)? c) Suppose before you ran this experiment, you thought it was equally likely that the claim was true or false. After running the experiment, what is your belief? What is the updated probability?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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