SOLUTION: 5.A manager hopes to improve the sales figures for 10 employees by sending them to a motivational seminar. To test the effectiveness of this seminar, the manager compares the sale

Question 135293: 5.A manager hopes to improve the sales figures for 10 employees by sending them to a motivational seminar. To test the effectiveness of this seminar, the manager compares the sales figures for each salesperson for the month immediately prior to the seminar and the month immediately following it.
Employee-------before--------after
Homer-----------19-----------12
Bart------------6------------18
Lisa------------9------------12
Marge-----------5------------7
Maggie----------9------------14
Ned-------------8------------17
Milhouse-------11------------9
Willie---------11------------17
Stu------------11------------12
Gill-----------7-------------7
Run a statistical hypothesis test and determine if the seminar significantly improved sales figures for the company.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A manager hopes to improve the sales figures for 10 employees by sending them to a motivational seminar. To test the effectiveness of this seminar, the manager compares the sales figures for each salesperson for the month immediately prior to the seminar and the month immediately following it.
Employee-------before--------after
Homer-----------19-----------12
Bart------------6------------18
Lisa------------9------------12
Marge-----------5------------7
Maggie----------9------------14
Ned-------------8------------17
Milhouse-------11------------9
Willie---------11------------17
Stu------------11------------12
Gill-----------7-------------7
Run a statistical hypothesis test and determine if the seminar significantly improved sales figures for the company.
---------------------------------------------
Create a difference column by forming (before-after) data.
You would be (19-12=7),(6-18=-12),(9-12=-3) etc.
Find the mean of those differences: d-bar=-2.9
and the standard deviation of the differences: s=5.4661
--------------------------------------
Ho: u(before)-u(after)=0
Ha: u(before)-u(after)<0 (claim)
--------------------------------
Critical value for one-tail z-test with alpha=5%: z= -1.645
-----------------------------------
Test statistic: z(-2.9) = (-2.9-0)/[5.4661/sqrt(10)]= -1.677723...
-------------------------------------
Conclusion: Since test stat lies in the rejection interval, Reject Ho.
Test provides statistical evidence favoring the claim.
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Cheers,
Stan H
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