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Hypothesis Test for a Population Proportion
A well-known brokerage firm executive claimed that \( 80 \% \) of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 200 people, \( 74 \% \) of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than \( 80 \% \) at the 0.01 significance level.
The null and alternative hypothesis would be:
\[
\begin{array}{cccccc}
H_{0}: \mu=0.8 & H_{0}: \mu \geq 0.8 & H_{0}: p \leq 0.8 & H_{0}: p=0.8 & H_{0}: \mu \leq 0.8 & H_{0}: p \geq 0.8 \\
H_{1}: \mu \neq 0.8 & H_{1}: \mu< 0.8 & H_{1}: p> 0.8 & H_{1}: p \neq 0.8 & H_{1}: \mu> 0.8 & H_{1}: p< 0.8
\end{array}
\]
The test is:
left-tailed two-tailed right-tailed \( o^{6} / \)