Carpetland salespersons average $8000 per week in sales. 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 conclude that the compensation plan increases the average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.: - Select your answer -: - Select your answer -b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - Select your answer - when in fact it does not.What are the consequences of making this error

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.

Step-by-step explanation:

This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.

The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.

We can write this hypothesis as:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.