Question

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.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 greaterthan 8000 (correct) 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

Answer 1

Explanation:

a) The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

From the given situation,

Carpetland salespersons average $8000 per week in sales. This is the null hypothesis.

H0: µ = 8000

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. This is the alternative hypothesis.

Ha: µ > 8000

b) A type I error occurs when a true null hypothesis is rejected.

In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales greater than 8000 (correct) when in fact it does not.

c) a Type II error would occur if it was concluded that the new compensation plan does not provide a population mean weekly sales greater than 8000 when in fact, it does.