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    IBHardStatistics10–12

    Hypothesis Testing

    Testes de Hipóteses

    A coin is tossed 2020 times and 1515 heads are observed. At a 5%5\% significance level, test the hypothesis that the coin is fair. Use X∼B(20,0.5)X \sim B(20, 0.5) and P(X≥15)≈0.0207P(X \ge 15) \approx 0.0207.

    Twenty-one separated vertical bars, one for each number of heads from 0 to 20, at their true relative heights, symmetric about a peak at 10 heads. A dashed vertical line stands just before 15 heads, and every bar from 15 upward is shaded darker to mark the region of 15 or more heads. The vertical axis is marked as the probability of k heads and carries no numeric scale.kP(X = k)05101520X ≥ 15

    H0H_0: p=0.5p = 0.5, H1H_1: p>0.5p > 0.5 (one-tailed). Compare P(X≥15)P(X \ge 15) with the significance level.

    Solution

    Step 1 of 4

    1. 1.H0H_0: p=0.5p = 0.5, H1H_1: p>0.5p > 0.5