Question

In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects 22 sales trainees who are randomly divided into two equal experimental groups—one receives type A and the other type B training. The salespeople are then assigned and managed without regard to the training they have received. At the year’s end, the manager reviews the performances of salespeople in these groups and finds the following results:

	A Group	B Group
Average Weekly Sales	x¯1x¯1 = $1,350	x¯2x¯2 = $1,086
Standard Deviation	s1 = 233	s2 = 263

(a) Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training.

H₀: µ_A ? µ_B ?  versus H_a: µ_A ? µ_B  >

(b) Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent. Assuming that the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part a at level of significance .10, .05, .01 and .001. How much evidence is there that type A training produces results that are superior to those of type B? (Round your answer to 3 decimal places.)

t =

(Click to select)RejectDo not reject H0 with ? equal to .10.

(Click to select)RejectDo not reject H0 with ? equal to .05

(Click to select)RejectDo not reject H0 with ? equal to .01

(Click to select)RejectDo not reject H0 with ? equal to .001

(Click to select)WeakVery strongExtremely strongStrongNo  evidence that µA ? µ B > 0

(c) Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used. Interpret this interval. (Round your answer to 2 decimal places.)

Confidence interval [, ]

Answer 1

Two-Sample T-Test and CI

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	11	1350	233	70
Sample 2	11	1086	263	79

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ > 0

test statistic t =

= 248.453

t = 2.492

degrees of freedom df = 11-1+11-1 = 20

critical values for alpha = 0.1

t_0.1,20 = 1.325

critical values for alpha = 0.05

t_0.05,20 = 1.725

critical values for alpha = 0.01

t_0.01,20 = 2.528

critical values for alpha = 0.001

t_0.001,20 = 3.552

Reject H₀ with alpha equal to .05, and conclude that there is a significant evidence that the difference between the means weekly sales obtained when type A training is used and weekly sales obtained when type B training is used is significantly different.

effect size cohen's d = = (1086 - 1350) ⁄ 248.453215 = 1.062574.

Very strong evidence that µ_A - µ _B > 0

c) 95 percent confidence interval

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
264	248	(43.0113, 484.9887)

The lower bound is 43.011 and the upper bound is 484.988. We are 95% confident the the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used. is between $43.011 and $484.988.