Problem
A study done on a marriage counselling course showed that the proportion of couples for which the communication program can prevent divorce is $80 \%$. Suppose we have strong reason to believe the proportion is less than $80 \%$, and we carry out a hypothesis test. State the null hypothesis $H_{0}$ and the alternative hypothesis $\mathrm{H}_{1}$ that we would use for this test. \[ \begin{array}{l} H_{0}: \mu \\ H_{1}: \square \end{array} \] \begin{tabular}{ccc} \hline$\mu$ & $\bar{x}$ & $p$ \\ $\hat{p}$ & $\sigma$ & $s$ \\ $\square$ & & $\square<\square$ \\ $\square \leq \square$ & $\square>\square$ & $\square \geq \square$ \\ $\square=\square$ & $\square \approx \square$ & \\ $X$ & & $\zeta$ \end{tabular} Try again Recheck Save For Later Submit Assigr
Solution
Step 1 ：The null hypothesis $H_{0}$ is a statement of no effect or no difference. In this case, it would be that the proportion of couples for which the communication program can prevent divorce is $80 \%$. So, $H_{0}$: $\mu = 80 \%$
Step 2 ：The alternative hypothesis $H_{1}$ is what we might believe to be true or hope to prove true. In this case, it would be that the proportion is less than $80 \%$. So, $H_{1}$: $\mu < 80 \%$
Step 3 ：\(\boxed{H_{0}: \mu = 80 \%}\)
Step 4 ：\(\boxed{H_{1}: \mu < 80 \%}\)
