Exercise 1

Fortitude Insurance sells extended car warranties over the phone. They call people using random dialing. When recipients of the phone call press one on their phone, they are transferred to a sales agent. Sales agents are paid on commission. Management is concerned about the rapid turn-over of sales agents. They have decided to test a more lucrative commission plan. You have been hired to conduct this test. The research question: Does the new commission plan help sales agents increase their weekly sales commission?The significance level will be set at 5%.

Step 1: Test Set-Up

Question 1:Howlarge a sample is needed to achieve 80% statistical power?Based on past research Cohen's d effect size is estimated at 0.40, which is a small effect. See the table below

Cohen's d ES Thresholds
Small	0.2
Medium	0.5
Large	0.8

Here are the results of an a priori power analysis run using G*Power.

Output parameters Noncentrality parameter 6 2.5612497 Critical t 1.6838510 Df 40 Total sample size 41 Actual power 0.8085822\fInput parameters Output parameters Tail(S) One Noncentrality parameter 6 2.4979992 Determine Effect size d 0.4 Critical t 1.6548084 a err prob 0.05 Df 154 Power (1-B err prob) 0.8 Sample size group 1 78 Allocation ratio N2/N1 7 Sample size group 2 78 Total sample size 156 Actual power 0.8001474