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After completing sales training for a large company, it is expected that a salesperson will generate a sale on more than 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of 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 76 of the calls.
-The correct value of the test statistic is
A) 2.24.
B) 1.96.
C) -2.24.
D) 3.34.
E) -1.645.

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion: $ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $, where $\hat{p} = \frac{76}{400} = 0.19$, $p_0 = 0.15$, and $n = 400$. Plugging in these values gives $ z = \frac{0.19 - 0.15}{\sqrt{\frac{0.15 \times 0.85}{400}}} = 2.24 $.

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