Question

Carpetland salespersons average $8,000 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.
Complete parts (b) and (c):
(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 ____________ when in fact it does not.
(c) In this situation, a Type II error would occur if it was concluded that the new compensation plan provides a population mean weekly sales ____________ when in fact it does not.

Answer 1

Explanation:

Hello!

The researcher claims that thanks to the new selling incentives the average sales per salesperson, symbolically: μ > $8000

The parameter of the study is the population mean sales per salesperson.

And the hypotheses:

a)

H₀: μ ≤ 8000

H₁: μ > 8000

b)

The type I error is committed when a true null hypothesis is rejected.

In terms of this problem, it is when is concluded that the new compensation plan provides a population mean of weekly sales is greater when in fact it does not.

c)

The type II error is committed when a false null hypothesis is not rejected.

In this case, it will be to conclude that the new compensation plan does not change the population mean of weekly sales when in reality it increases them.

I hope this helps!