Determine the standardized test statistic, $z$, to test the claim about the populatio proportion $p \geq 0.132$ given $n=48$ and $\hat{p}=0.11$ Use $\alpha=0.05$.
Answer
Final Answer: The standardized test statistic, $z$, is \(\boxed{-0.45029432259193036}\).
Step 1 ：We are given the population proportion $p = 0.132$, the sample size $n = 48$, and the sample proportion $\hat{p} = 0.11$. We are asked to find the standardized test statistic, $z$, using the formula: $$z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$$
Step 2 ：Substitute the given values into the formula: $$z = \frac{0.11 - 0.132}{\sqrt{\frac{0.132(1-0.132)}{48}}}$$
Step 3 ：Solving the above expression, we find that the standardized test statistic, $z$, is approximately -0.45029432259193036.
Step 4 ：Final Answer: The standardized test statistic, $z$, is \(\boxed{-0.45029432259193036}\).
