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Chapter 8: Problem 80

Suppose you tested 50 coins by flipping each of them many times. For each coin, you perform a significance test with a significance level of \(0.05\) to determine whether the coin is biased. Assuming that none of the coins is biased, about how many of the 50 coins would you expect to appear biased when this procedure is applied?

Short Answer

Expert verified
The expected number of unbiased coins which may falsely appear as biased due to statistical testing is approximately is either 2 or 3.

Step by step solution

01

Understand the concept

Firstly, it is essential to understand the significance level which is the probability of rejecting the null hypothesis when it is true. It is the risk taken in using a hypothesis test and in this problem, it is given as 0.05 or 5%.
02

Calculate expected value

In this problem, each coin is a trial and the event 'appearing to be biased' is determined for each coin. Therefore, each coin is a Bernoulli trial and we can calculate the expected value. With 50 coins flipped, the expected number of coins which would appear biased by the testing procedure is 50 times the risk of false rejection which is 50 * 0.05.
03

Final result

Multiply the number of trials (50 coins) by the probability a coin appears biased when it is not (0.05). The expected number of coins that would appear biased is \(50 * 0.05 = 2.5 \). However, since we can't have 0.5 of a coin, we would expect either 2 or 3 coins to falsely appear biased due to the number of trials.

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Most popular questions from this chapter

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