Question

Question: For each of the following scenarios, conduct the complete hypothesis testing process as appropriate give that scenario.

A regional manager implements a policy change for stores in his region to begin greeting customers whenever they are standing within a 3 metre distance in the store. He compares mean daily purchase numbers over one month from pre-change to post-change for each store to see if the change makes a difference in sales.

            Mean daily purchases for Store 1 through Store 10 before policy: 82, 103, 91, 91, 83, 76, 90, 114, 88, 92

            Mean daily purchases for Store 1 through Store 10 after policy: 102, 83, 113, 87, 94, 78, 91, 117, 101, 107

Answer 1

Ho :   µd=   0
Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
82	102	-20.000	187.69
103	83	20.000	691.69
91	113	-22.000	246.49
91	87	4.000	106.09
83	94	-11.000	22.09
76	78	-2.000	18.49
90	91	-1.000	28.09
114	117	-3.000	10.89
88	101	-13.000	44.89
92	107	-15.000	75.69

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	910	973	-63	1432.1

mean of difference ,    D̅ =ΣDi / n =   -6.300                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    12.6144                  
                          
std error , SE = Sd / √n =    12.6144   / √   10   =   3.9890      
                          
t-statistic = (D̅ - µd)/SE = (   -6.3   -   0   ) /    3.9890   =   -1.579
                          
Degree of freedom, DF=   n - 1 =    9                  
p-value =        0.14872   [excel function: =t.dist.2t(t-stat,df) ]               
Conclusion:     p-value>α=0.05 , Do not reject null hypothesis     

There is not enough evidence to conclude that   the change makes a difference in sales at α=0.05