A large car dealership with 20 locations nationwide is interested in implementin

Question

A large car dealership with 20 locations nationwide is interested in implementing a training program to increase the sales of its workers. A human resources consulting firm offers a variety of training programs which vary in technique and duration. After evaluating all proposals, the owners have narrowed it down to three possible training programs but disagree on which one would be more effective. Consider you want to help in making an informed decision and propose a way to statistically test the effectiveness of the three training programs by collecting data from three different dealer locations: Houston, San Antonio and Dallas. Write one or two short paragraphs explaining the owners how you would do this. In your answer make sure to include the following.

Briefly explain how you would organize the experiment to evaluate the effectiveness of the three different training programs.

What test statistic would you use?

What is the specific question you will be able to answer with your proposed method?

What are the sample elements from which you will collect the data?

What is the random variable to use as a measure of the effectiveness of the programs?

What sample statistics you would need to calculate in order to be able to test this?

Explanation / Answer

To have an informed decision, data on various techniques and duration on three possible training programs are to be collected to statistcally test the effectiveness of the three training programs. The owner should collect data on techniques and duration from different dealer's location viz., Houston, San Antonio and Dallas.

In order to test the difference of quality of training we can use paired t-test for difference of means. Suppose we want to test the difference of tecniques between the two trainings, we can take datas say xi be the technique ( may be the number of persons interviewed ) and yi be the number of hours of trainings. and di = xi - yi

Under the null hypothsis, H0 that increments are due to fluctuation of sampling, i.e., the difference of technique is not responsible for these increments, the statistic t = (Mean of di)/S/n.

where = 1/n di, S2 = 1/n-1 (di - )2

Follows Student's t distribution with (n-1) degrees of freedom.

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