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mathmari

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A and B play 100 games of squash; A wins E times. B claims that both of them have the same probability of winning a game.

We consider that the games are independent.

(a) Formulate the null hypothesis and the alternative hypothesis.

(b) For which values of $E$ will the null hypothesis be rejected with $\alpha=1\%$ and for which with $\alpha=5\%$ ?Is at (a) the null hypothesis $H_0: \ p=\frac{1}{2}$ and the alterinative hypothesis $H_1: \ p\neq \frac{1}{2} $ ? Or do we call $p_A$ the probability of $A$ and $p_B$ the probability of $B$, and so the null hypothesis is $H_0: \ p_A=p_B$ and the alterinative hypothesis $H_1: \ p\_A\neq p_B $ ? (Wondering)