Question

nA car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $4600, and takes a random sample of 16 of the new salesperson's sales and finds an average markup of $4100 with a standard deviation of $500. What is the value of an appropriate test statistic for the car dealer to use? Multiple Choice -4 4 -3 3

Answer 1

Answer:

The value of an appropriate test statistic for the car dealer to use is -4.

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 4600$

The alternate hypotesis is:

$H_{1} < 4600$

The test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

In this problem:

$X = 4100, \mu = 4600, \sigma = 500, n = 16$

Then

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{4100 - 4600}{\frac{500}{\sqrt{16}}}$

$t = -4$

The value of an appropriate test statistic for the car dealer to use is -4.