Estrus synchronization products are used to bring cows into heat at a predictable time so that they can be reliably impregnated by artificial insemination. In a study of two estrus synchronization products, 42 mature cows (ages 4-8 years) were randomly allocated to receive either product A or product $\mathrm{B}$, and then all cows were bred by artificial insemination. The table shows how many of the inseminations resulted in pregnancy. ${}^8$ Consider a chi-square test to compare the effectiveness of the two products in producing pregnancy.Here is computer output for a chi-square test using a nondirectional alternative.$X$ -squared $=4.71,df=1,$ p-value $=0.03$(a) State the null and alternative hypotheses in context.(b) Compute the expected frequencies.(c) If $\alpha =0.05,$ what is your conclusion regarding $H_0?$(d) Suppose that prior to conducting the study, the researchers were expecting product A to be superior to product B. Using $\alpha =0.05$ and a directional alternative, what is your conclusion?

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