Question

A company recently switched its compensation plan. Prior to the switch, salespeople were paid a higher salary, but their commission on each item sold was smaller. After the switch, the salary was less, but the commission for each item sold was larger. A complaint was lodged with HR with the threat of legal action claiming the sales team was making less money. The HR director examined the salaries of nine randomly selected salespeople. Their salaries ($1000’s) before and after the switch are shown in the table below.

Salesperson 1 2 3 4 5 6 7 8 9

Before 55 22 34 22 25 61 55 36 68

After 53 24 36 28 31 61 58 38 72

(a) Is there evidence that salaries decreased under the new compensation plan? Test at the 2.5% level of significance.

(b) Explain the meaning of the P-value in the context of the study.

(c) Explain the meaning of a Type I error in the context of the study.

(d) Explain the meaning of a Type II error in the context of the study.

Answer 1