Exercise Solution 4.7

We will toss the coin a hundred times and observe the number of heads, so S = X[1] + X[2] + … + X[100]. Assuming , S ~ B(100, 0.5), which we can use to calculate probabilities. We wish to specify a non-rejection region such that, assuming  is true, there is no more than a 0.01 probability of inadvertently rejecting . Based on the B(100, 0.5) CDF, we determine that the closed interval [37, 62] is such a region. See the downloadable spreadsheet for calculations. Our test is then to toss the coin a hundred times, observe the number s of heads, and reject the coin as not fair if s < 37 or if s > 62.

As indicated in the spreadsheet, another reasonable non-rejection region would be interval [38, 63].