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: 

A Group  B Group  
Average Weekly Sales  x¯1x¯1 = $1,574  x¯2x¯2 = $1,135 
Standard Deviation  s_{1} = 230  s_{2} = 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. 
H_{0}: 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 H_{0} with α equal to .10. 
(Click to select)RejectDo not reject H_{0} with α equal to .05 
(Click to select)Do not rejectReject H_{0} with α equal to .01 
(Click to select)Do not rejectReject H_{0} 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 [, ] 
a)
H_{0}: 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 Sp^{2}=((n_{1}1)s^{2}_{1}+(n_{2}1)*s^{2}_{2})/(n_{1}+n_{2}2)=  69082.0000 
std. error se =S_{p}*√(1/n1+1/n2)=  112.0730  
test stat t =(x1x2Δo)/Se=  3.917 
Reject H_{0} with α equal to .10.
Reject H_{0} with α equal to .05
Reject H_{0} with α equal to .01
Reject H_{0} with α equal to .001
. . Extremely strong evidence that µ_{A} − µ _{B} > 0
c)
point estimate of difference=x1x2=  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 differenceE=  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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