Question

Kitchen salespersons average $10,000 per week in sales. Manager proposes a compensation plan with new selling incentives. Manager hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. Required:a. Develop the appropriate null and alternative hypotheses. b. What is the type I error in this situation? What are the consequences of making this error? c. What is the type II error in this situation? What are the consequences of making this error?

Answer 1

a) The alternative hypothesis has to reflect the claim that the research want to test. In this case, we want to test if there is enough evidence that the incentives increase the average sales per salesperson.

That is, if the average sales are significantly higher than $10,000 per salesperson.

The null hypothesis will state that the average sales per salesperson is not significantly higher than $10,000, representing the base case.

Then, we can write the hypothesis as:

`H_0: \mu=10,000\\\\H_a: \mu>10,000`

b) A Type I error happens when a true null hypothesis is rejected.

In this case, it would represent concluding that the incentive program is effective in increasing sales when it is not really the case.

The significative difference would be only due to chance and not to a real difference.

c) A Type II error happens when a false null hypothesis failed to be rejected.

In this case, it would represent that the sample statistic gives no enough evidence to support the claim that the incentive program is effective, although it is, in fact, effective. The conclusion will be, erroneously, that the program of incentives is not effective.

Explanation: