Problem

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $(\mu, \rho, \sigma)$ for the indicated parameter.

A psychologist claims that more than $5.8 \%$ of the population suffers from professional problems due to extreme shyness. Use $p$, the true percentage of the population that suffers from extreme shyness.
A.
\[
\begin{array}{l}
H_{0}: p=5.8 \% \\
H_{1}: p> 5.8 \%
\end{array}
\]
B.
\[
\begin{array}{l}
H_{0}: P=5.8 \% \\
H_{1}: P \geq 5.8 \%
\end{array}
\]
c.
\[
\begin{array}{l}
H_{0}: p=5.8 \% \\
H_{1}: p< 5.8 \%
\end{array}
\]

Answer

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Answer

Final Answer: \[\boxed{\begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p>5.8 \% \end{array}}\]

Steps

Step 1 :Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $(p)$ for the indicated parameter.

Step 2 :The null hypothesis is a statement of no effect or no difference and is assumed to be true until statistical evidence suggests otherwise. In this case, the null hypothesis would be that the true percentage of the population that suffers from extreme shyness is equal to 5.8%.

Step 3 :The alternative hypothesis is a statement that contradicts the null hypothesis. It is what you might believe to be true or hope to prove true. In this case, the psychologist claims that more than 5.8% of the population suffers from extreme shyness. So, the alternative hypothesis would be that the true percentage of the population that suffers from extreme shyness is greater than 5.8%.

Step 4 :Therefore, the correct symbolic form of the null hypothesis and the alternative hypothesis is: \[\begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p>5.8 \% \end{array}\]

Step 5 :Final Answer: \[\boxed{\begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p>5.8 \% \end{array}}\]

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