Question

The average number of sales at a car dealership is 24 with a standard deviation of 5. A week ago, you were promoted to manager. Over this week (seven days), the average number of sales has dipped to 20. Your boss says he is coming by tomorrow to check out how you have been doing. You know that your boss has a rule where he will fire any manager if the average number of sales is statistically lower than 24 with 99% confidence. Are you going to get fired? Complete a one sided hypothesis test.

Z =

p =

Critical Value =

Alpha =

Are you going to get fired?

No /Yes

Answer 1

Solution:

Given ,

= 24

= 5

n = 7

= 20

claim : < 24

Hypothesis can be written as

H0 : = 24 (null hypo.)

H1 :   < 24

1)

The test statistic z is given by

z =

= (20 - 24) / (5/7)

= -2.117

The test statistic is z = -2.117

2)p value

observe that ,there is < sign in H1. So , the test is left tailed.

p value = P(Z < -2.117) = 0.0171 (use z table)

p value = 0.0171

3)Given , c = 99% = 0.99

Alpha = = 1- c = 1 - 0.99 = 0.01

The critical value is - i.e. -_{0.01 = - 2.326 (Use z table)}

₄₎ z = -2.117

-_{0.01 = - 2.326}

z = -2.117 is greater than _{- 2.326}

_{So , we fail to reject the null hypothesis.}

_So, is not significantly less than 24.

Are you going to get fired?  

No