according to a university center for logistic...
according to a university center for logistics management, 8% of all merchandise sold in the united states gets returned. a seattle department store sampled 85 items sold in january and found that 5 of the items were returned.\n\nif you have the following null and alternative hypotheses for a test you are running:\n\n$h_0: p = 0.08$\n$h_a: p < 0.08$\n\ncalculate the test statistic, rounded to 3 decimal places\n$z =$
Answer
# Explanation:
## Step1: Calculate sample proportion
The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 5$ (number of returned items) and $n=85$ (sample - size). So, $\hat{p}=\frac{5}{85}\approx0.0588$.
## Step2: Recall the formula for the z - test statistic
The formula for the z - test statistic in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$, where $p_0 = 0.08$ (null hypothesis proportion), $\hat{p}$ is the sample proportion, and $n$ is the sample size.
## Step3: Substitute values into the formula
$z=\frac{0.0588 - 0.08}{\sqrt{\frac{0.08\times(1 - 0.08)}{85}}}=\frac{- 0.0212}{\sqrt{\frac{0.08\times0.92}{85}}}=\frac{-0.0212}{\sqrt{\frac{0.0736}{85}}}=\frac{-0.0212}{\sqrt{0.000865882}}\approx\frac{-0.0212}{0.0294}\approx - 0.721$.
# Answer:
$-0.721$