Problem

A study done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is $78 \%$. Suppose we have strong reason to believe the proportion is less than $78 \%$, and we carry out a hypothesis test. State the null hypothesis $\mathrm{H}_{0}$ and the alternative hypothesis $H_{1}$ that we would use for this test.
\[
\begin{array}{l}
H_{0}: \square \\
H_{1}: \square
\end{array}
\]

Answer

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Answer

\[\begin{array}{l}H_{0}: \text{The proportion of couples for which the communication program can prevent divorce is } 78 \% \H_{1}: \text{The proportion of couples for which the communication program can prevent divorce is less than } 78 \%\end{array}\]

Steps

Step 1 :State the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$ for the test.

Step 2 :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 $78 \%$.

Step 3 :The alternative hypothesis $H_{1}$ is what we are testing against the null hypothesis. In this case, it would be that the proportion is less than $78 \%$.

Step 4 :\[\begin{array}{l}H_{0}: \text{The proportion of couples for which the communication program can prevent divorce is } 78 \% \H_{1}: \text{The proportion of couples for which the communication program can prevent divorce is less than } 78 \%\end{array}\]

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