22.1 Coin tossing. We do not have the patience of Count Buffon, so we tossed a coin only 50 times. We got 21 heads. The proportion of heads is

This is less than one-half. Is this evidence that our coin is not balanced? Formulate the hypotheses for an appropriate significance test and determine the sampling distribution of the sample proportion of heads if the null hypothesis is true. As you are working through this problem, think about what you learned in Chapters 17 and 20 about the “law of large numbers.” Does it make sense that your sample proportion would be different with a smaller sample size?