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 = $1,574	x¯2x¯2 = $1,135
Standard Deviation	s1 = 230	s2 = 292

(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)Do not rejectReject H₀ with α equal to .10.

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

  (Click to select)Do not rejectReject H₀ with α equal to .01

  (Click to select)Do not rejectReject H₀ with α equal to .001

  (Click to select)WeakNoExtremely strongStrongVery strong  evidence that µ_A − 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

a)

H₀: µ_A − µ_B ≤0 versus H_a: µ_A − µ_B  > 0

b)

	A	B
sample mean x =	1574.00	1135.00
standard deviation s=	230.000	292.000
sample size n=	11	11
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			69082.0000

std. error se =Sp*√(1/n1+1/n2)=		112.0730
test stat t =(x1-x2-Δo)/Se=		3.917

Reject H₀ with α equal to .10.

Reject H₀ with α equal to .05

Reject H₀ with α equal to .01

Reject H₀ with α equal to .001

. . Extremely strong evidence that µ_A − µ _B > 0

c)

point estimate of difference=x1-x2=		439.000
for 95 % CI & 20 df value of t=		2.086	from excel: t.inv(0.975,20)
margin of error E=t*std error =		233.7843
lower bound=mean difference-E=		205.2157
Upper bound=mean differnce +E=		672.7843
from above 95% confidence interval for population mean =(205.22 , 672.78)