Question

# In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a...

 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: µA − µB ≤  versus Ha: µA − µB  >

 (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 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 [, ]

a)

H0: µAµB ≤0 versus Ha: µAµB  > 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 µAµ 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)

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