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

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

Explanation:

The null hypothesis is:

`H_(0) = 4600`

The alternate hypotesis is:

`H_(1) < 4600`

The test statistic is:

`t = (X - \mu)/((\sigma)/(√(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 = (X - \mu)/((\sigma)/(√(n)))`

`t = (4100 - 4600)/((500)/(√(16)))`

`t = -4`

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