1. **State the problem:** We want to test the hypothesis $H_0: p = 0.20$ versus $H_a: p > 0.20$ using a z-test for a population proportion. 2. **Formula for the test statistic:** The z-test statistic for a proportion is given by $$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$ where $\hat{p}$ is the sample proportion, $p_0$ is the null hypothesis proportion, and $n$ is the sample size. 3. **Important rules:** - Use $p_0$ (the null hypothesis proportion) in the denominator to calculate the standard error. - The numerator is $\hat{p} - p_0$ because we measure how far the sample proportion is from the null. - Since $H_a$ is $p > 0.20$, the numerator should be $\hat{p} - p_0$ (not reversed). 4. **Given values:** - $\hat{p} = 0.24$ - $p_0 = 0.20$ - $n = 150$ 5. **Plug values into the formula:** $$z = \frac{0.24 - 0.20}{\sqrt{\frac{0.20 \times 0.80}{150}}}$$ 6. **Check options:** - Option D matches this formula exactly. **Final answer:** Option D $$z = \frac{0.24 - 0.20}{\sqrt{\frac{0.20 \times 0.80}{150}}}$$