In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A)-1.645
B)-2.066
C)-2.000
D)-1.960

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{24}{64} = 0.375$, $p_0 = 0.5$, and $n = 64$. Plugging these values into the formula gives $z = \frac{0.375 - 0.5}{\sqrt{\frac{0.5(0.5)}{64}}} = -2.000$.

In the Nation of Gondor, the EPA Requires That Half