It is claimed that in a bushel of peaches,fewer than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-test statistic?
A)+0.125
B)+0.278
C)−1.645
D)+1.667

Question

Quizplus · Accepted Answer

The z-test statistic is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{50}{400} = 0.125$, $p_0 = 0.10$, and $n = 400$. Plugging these values into the formula gives $z = \frac{0.125 - 0.10}{\sqrt{\frac{0.10(1-0.10)}{400}}} = +1.667$.

It Is Claimed That in a Bushel of Peaches,fewer Than