The Virginia Department of Environmental Quality (VDEQ) uses probabilistic monitoring to regulate the water quality of streams in the Commonwealth of Virginia. Of the 85 Eastern Virginia Sites (group 1), 17 do not meet minimum requirements. Of the 80 units sampled in Western Virginia Sites (group 2), 24 do not meet minimum requirements. Assume the data can be treated as independent simple random samples. What is the value of the z test statistic for testing the equality of the proportions of streams that fail to meet minimum requirements in the two areas?

Question

Quizplus · Accepted Answer

To calculate the z test statistic for the difference between two proportions, we use the formula: $$z = \frac{p_1 - p_2}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}}$$ where $p_1$ and $p_2$ are the sample proportions of streams that fail to meet minimum requirements in the Eastern and Western Virginia Sites, respectively, $n_1$ and $n_2$ are the sample sizes, and $p$ is the combined proportion of streams that fail to meet the requirements. Given:- $n_1 = 85$, $n_2 = 80$- Number of failures in Eastern Virginia (group 1) = 17, so $p_1 = \frac{17}{85}$- Number of failures in Western Virginia (group 2) = 24, so $p_2 = \frac{24}{80}$- Combined failures = 17 + 24 = 41- Combined sample size = 85 + 80 = 165- Combined proportion $p = \frac{41}{165}$Plugging these values into the formula gives a z value of approximately -1.49, indicating that the correct choice is A.

The Virginia Department of Environmental Quality (VDEQ) Uses Probabilistic Monitoring