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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
We would expect approximately \(2\) to \(3\) of the 50 coins to appear biased by this procedure, even though none of them is actually biased.

Step by step solution

01

Understanding the Concept

The significance level of \(0.05\) essentially means there's a \(5\%\) chance of making a Type I error, that is, rejecting a true null hypothesis. Here, the null hypothesis is that the coin is not biased. So, a result indicating bias is essentially a Type I error.
02

Calculating the Number of Coins

To calculate the expected number of coins exhibiting bias (making a Type I error), simply multiply the total number of coins by the probability of making a Type I error (the significance level). That is, \(50\) coins times \(5\%\) chance of a Type I error.
03

Performing the Calculation

By performing the calculation: \(50 \times 0.05 = 2.5\). However, since we can't have half of a coin, we conclude that approximately \(2\) or \(3\) (rounding up) coins would appear to be biased due to statistical fluctuation.

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