To express the null hypothesis ([tex]\(H_0\)[/tex]) and the alternative hypothesis ([tex]\(H_1\)[/tex]) in symbolic form given that a researcher claims that 62% of voters favor gun control, we use the parameter [tex]\( p \)[/tex], which represents the proportion of voters favoring gun control.
We start with the claim that the proportion [tex]\( p \)[/tex] is equal to 0.62. This translates to:
- The null hypothesis ([tex]\(H_0\)[/tex]) represents the initial assumption or the default claim. Here, it will state that the proportion is equal to 0.62.
- The alternative hypothesis ([tex]\(H_1\)[/tex]) represents what we want to test against the null hypothesis. Since the problem states a specific value (0.62), we use a two-tailed test notation. Therefore, [tex]\(H_1\)[/tex] will state that the proportion is not equal to 0.62.
In symbolic form, the hypotheses can be expressed as:
[tex]\[
\begin{array}{l}
H_0: p = 0.62 \\
H_1: p \neq 0.62
\end{array}
\][/tex]
This is the correct way to express the hypotheses given the researcher's claim.
