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. \[ \begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p \leq 5.8 \% \end{array} \] B. \[ \begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p<5.8 \% \end{array} \] c. \[ \begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p>5.8 \% \end{array} \] D. $\mathrm{H}_{0}: \mathrm{p}=5.8 \%$ \[ H_{1}: p \geq 5.8 \% \]
Solution
Step 1 ：The null hypothesis is usually 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 true percentage of the population that suffers from extreme shyness is equal to 5.8%.
Step 2 ：The alternative hypothesis is what you might believe to be true or hope to prove true. In this case, since the psychologist claims that more than 5.8% of the population suffers from professional problems due to extreme shyness, the alternative hypothesis would be that the true percentage of the population that suffers from extreme shyness is greater than 5.8%.
Step 3 ：Therefore, the correct symbolic form for the null hypothesis and the alternative hypothesis would be: \[\begin{array}{l} H_{0}: p=5.8 \% \\ H_{1}: p>5.8 \% \end{array}\]
Step 4 ：So, the final answer is C.
