Question

A manager in a rapidly growing industry wishes to study the effects of motivation on sales in particular firm. Traditionally, all sales staff has been salaried. Senior management has been most reluctant to change the existing system. Within his own branch, however, the manager wishes to gather evidence on whether or not to pay commissions to salespersons. Of 24 new salespersons, 12 are paid an hourly rate and 12 are paid a commission. The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the first month on the job.

Hourly	Commission
256	224
239	254
222	273
207	285
228	237
241	277
212	261
216	228
236	234
219	225
225	232
230	245

1. Is there evidence that commission and hourly rate sales differ? Use Excel, a = .01, and the p-value approach to answer this question. Attach your Excel analysis to your assignment answers.                                                                  

1. Hyps: H₀:

H₁:

2. Test(s):

3. Analysis:

p-value:

4. Conclusions: (1)

(2)

(3)

(4)

What assumptions must be made in part (a) of this problem?

Answer 1

using excel>data>data analysis>two sample t

we have

t-Test: Two-Sample Assuming Equal Variances
	Hourly	Commission
Mean	227.5833	247.9167
Variance	191.5379	466.0833
Observations	12	12
Pooled Variance	328.8106
Hypothesized Mean Difference	0
df	22
t Stat	-2.7467
P(T<=t) one-tail	0.005887
t Critical one-tail	1.717144
P(T<=t) two-tail	0.011774
t Critical two-tail	2.073873

1. Hyps: H₀:

H₁:

2. Test(s): here we will use t test for two independent samples

3. Analysis: t test =-2.7467

p-value:0.0118

4. Conclusions: (1) since p-value is greater than 0.01 so we do not reject the null hypothesis

(2) No there is no evidence that commission and hourly rate sales differ

assumptions : samples are taken randomly, variances are equal and both the samples are normally distributed