Step 1 :1. Calculate the sample proportion ($\hat{p}$) and its complementary proportion ($1-\hat{p}$): $\hat{p}=\frac{24}{58}$, $1-\hat{p}=\frac{34}{58}$
Step 2 :2. Calculate the standard error (SE) using the assumed population proportion ($p_0 = 0.3$) and sample size (n=58): $\mathrm{SE}=\sqrt{\frac{p_0(1-p_0)}{n}}=\sqrt{\frac{0.3(1-0.3)}{58}}$
Step 3 :3. Calculate the test statistic: $z=\frac{\hat{p}-p_0}{\mathrm{SE}}=\frac{\frac{24}{58}-0.3}{\sqrt{\frac{0.3(1-0.3)}{58}}}$
Step 4 :4. Using a standard normal (z) distribution table, find the p-value for (${z}$): $p$-value
Step 5 :5. Compare $p$-value to the given significance level ($\alpha=0.01$): Less than (or equal to) $\alpha$ or Greater than $\alpha$