Question

In: Statistics and Probability

Carpetland salespersons average $8000 in sales per week. Steve Contois, the firm’s vice president, proposes a...

Carpetland salespersons average $8000 in sales per week. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to test whether the compensation plan would be effective. Before answering the following questions, you will need to first formulate the appropriate null and alternative hypotheses. a. What is the Type I error in this situation? What are the consequences of making this error? b. What is the Type II error in this situation? What are the consequences of making this error? c. Since there is money involved in the proposed plan, Steve would like to have a more stringent test by imposing a lower significance level. As a student of Statistics, do you think this is a good idea? Explain.

Solutions

Expert Solution

Steve hopes that the results of a trial selling period will enable him to test whether the compensation plan would be effective

This means that the alternate hypothesis in this case will be that the average is more than $8,000

So, we can write

(A) We know that type I error is rejecting the true null hypothesis. In this case, type I error will be the conclusion that average sales is increased or compensation plan is effective, when actually it is less than or equal to $8000 or the compensation plan is not effective. This will result in extra incentives to sales person who have low performance.  

(B) we know that type II error is failing to reject the false null hypothesis. In this case, type II error will be the conclusion that the average sales is not increased or compensation plan is not effective, when actually the sale is increased or compensastion plan is effective. This will result in no incentives to those sales person who have shown high performance or worked better than other.

(C) yes, this is a good idea as we know that by lowering the significance level, the chances of rejecting the true null hypothesis also get reduced. This means that we will have a more conservative result as compared to higher significance level.

orchestra answered 10 months ago
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