After completing sales training for a large company, it is expected that the salesperson will generate a sale on at least 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of n = 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 36 of the calls. Based on this information, what is the test statistic for this test?
A) Approximately 0.1417
B) About z = -3.35
C) z = -1.645
D) t = -4.567

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion z-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, $\hat{p} = \frac{36}{400} = 0.09$, $p_0 = 0.15$, and $n = 400$. Plugging these values into the formula gives a z-value of approximately -3.35, indicating the test statistic for this hypothesis test.

After Completing Sales Training for a Large Company, It Is