Question

less than 58% of people support the death penalty. express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
$h_0:p$
$h_1:p$
use the following codes to enter the following symbols:
$\geq$ enter $>=$
$\leq$ enter $<=$
$\
eq$ enter $!=$
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Explanation:

Step1: Define the null hypothesis

The null hypothesis \(H_0\) is a statement of no difference or no effect. It assumes that the claim is not true. Here, the claim is about the proportion \(p\) of people supporting the death penalty. The null hypothesis for a proportion - related claim (when the alternative is one - sided) is usually \(H_0:p = p_0\), where \(p_0\) is the value in the non - alternative situation. So, \(H_0:p=58\%\) (or \(H_0:p = 0.58\) in decimal form, but since the question asks for percentage, we use \(58\%\)).

Step2: Define the alternative hypothesis

The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. The claim is “Less than 58% of people support the death penalty”. So, \(H_1:p<58\%\) (using the code \(<=\) for \(\leq\) is incorrect as the claim is strictly less than. Using the code \(<\) which is represented as \(<=\) in the given code (but actually for strict inequality in hypothesis testing for proportions when the claim is “less than”, we use \(p < p_0\)).

Answer:

\(H_0:p = 58\%\)
\(H_1:p<58\%\)