Problem

Question 1
$79 \%$ of people support legalizing gay marriage. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
\[
\begin{array}{l}
H_{0}: p \\
H_{a}: p
\end{array}
\]

Use the following codes to enter the following symbols:
\[
\begin{array}{l}
\geq \text { enter }> = \\
\leq \text { enter }< = \\
\neq \text { enter != }
\end{array}
\]

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Final Answer: \(\boxed{H_{0}: p \neq 0.79}\) , \(\boxed{H_{a}: p = 0.79}\)

Steps

Step 1 :The null hypothesis (H0) is a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove. In this case, the null hypothesis would be that the proportion of people who support legalizing gay marriage is not 79%.

Step 2 :The alternative hypothesis (Ha) is a statement of an effect or difference. It is the hypothesis that the researcher is trying to prove. In this case, the alternative hypothesis would be that the proportion of people who support legalizing gay marriage is 79%.

Step 3 :Since the question asks to express the hypotheses in symbolic form, we can use 'p' to represent the proportion of people who support legalizing gay marriage.

Step 4 :So, the null hypothesis would be H0: p != 0.79 (the proportion of people who support legalizing gay marriage is not 79%) and the alternative hypothesis would be Ha: p = 0.79 (the proportion of people who support legalizing gay marriage is 79%).

Step 5 :Final Answer: \(\boxed{H_{0}: p \neq 0.79}\) , \(\boxed{H_{a}: p = 0.79}\)

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