5-1 Probability Distributions 211 Identification of significantly low or significantly high numbers of successes is sometimes used for the purpose of rejecting assumptions, as stated in the following rare event rule. The Rare Event Rule for Inferential Statistics If, under a given assumption, the probability of a particular outcome is very small and the outcome occurs significantly less than or significantly greater than what we expect with that assumption, we conclude that the assumption is probably not correct. For example, if testing the assumption that boys and girls are equally likely, the outcome of 20 girls in 100 births is significantly low and would be a basis for rejecting that assumption. FIGURE 5-4 Probability Histogram of Heads in 460 Coin Tosses continued Identifying Significant Results with Probabilities EXAMPLE 5 Is 252 heads in 460 coin tosses a significantly high number of heads? What does the result suggest about the Chapter Problem, which includes results from 460 overtime games between 1974 and 2011? (Among the 460 teams that won the coin toss, 252 of them won the game. Is 252 wins in those 460 games significantly high?) A result of 252 heads in 460 coin tosses is greater than we expect with random chance, but we need to determine whether 252 heads is significantly high. Here, the relevant probability is the probability of getting 252 or more heads in 460 coin tosses. Using methods covered later in Section 5-2, we can find that P(252 or more heads in 460 coin tosses) = 0.0224 (rounded). Because the probability of getting 252 or more heads is less than or equal to 0.05, we conclude that 252 heads in 460 coin tosses is a significantly high number of heads. See Figure 5-4, which is a probability histogram showing the probability for the different numbers of heads. SOLUTION CP
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