2. The vice president of marketing brought to the attention of sales managers th

Question

2.   The vice president of marketing brought to the attention of sales managers that most of the company’s sales representatives maintained client relationships in a disorganized, haphazard way. The sales managers brought the sales representatives in for a three-day seminar and training session on how to use an organizer to schedule visits and recall pertinent information about each client more effectively. Following are data on the number of visits by sales reps on two randomly selected days, one before the training seminar and one after the seminar. Test whether significantly more site visits were made after the seminar (alpha = .05).

Rep   No. of visits before   No. of visits after
1       2           4
2       4           5
3       1           3
4       3           3
5       4           3
6       2           5
7       2           6  
8       3           4
9       1           5

a.   Ho:                Ha:

T = ?    P = ?       Conclusion?

Were significantly more site visits made after the seminar?    Yes   No

Explanation / Answer

The differences are

2
1
2
0
-1
3
4
1
4

Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0   [ANSWER]

**************************************

At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    1.66969422          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.55656474          
              
Calculating the mean of the differences (third column):              
              
XD =    1.777777778          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    3.194197638   [ANSWER, T]

***********************************      
              
As df = n - 1 =    8          
              
Also, using p values, as it is right tailed,              
              
p =        0.006361416   [ANSWER, P VALUE]

*************************************  
              
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.      

YES, significantly more site visits made after the seminar. [ANSWER, YES]

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