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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

Respuesta :

Answer:

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

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 4600[/tex]

The alternate hypotesis is:

[tex]H_{1} < 4600[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

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

In this problem:

[tex]X = 4100, \mu = 4600, \sigma = 500, n = 16[/tex]

Then

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{4100 - 4600}{\frac{500}{\sqrt{16}}}[/tex]

[tex]t = -4[/tex]

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

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