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A consumer advocacy group feels that Walmart provides a less safe shopping envir

ID: 3150386 • Letter: A

Question

A consumer advocacy group feels that Walmart provides a less safe shopping environment than Target. To try to prove their point, they randomly selected 20 Walmart stores and found the annual number of crime reports filed for these stores. Each of these Walmart stores was then paired with a Target store within a 10 mile radius, and the annual crime reports for the associated Target stores were also recorded. The data is shown below. Test to to see if the mean number of crime incidents at Walmart stores is significantly larger than the mean number of crime incidents at Target stores. Please note the data shown below is not real, but if you would like to see the real example, check out walmartcrimereport.com. Unfortunately, the real data was collected in a way that was not fair to Walmart. Assume normality.


A) Let W represent the mean incidents associated with Walmart, and let T represent the mean incidents associated with Target. What are the proper hypotheses?

a) H0: W = T versus Ha: W T

b) H0: W = T versus Ha: W > T    

c) H0: W = T versus Ha: W < T

d) H0: W = T versus Ha: W = T



B) What is the test statistic? Give your answer to four decimal places.  

C) Using a 0.05 level of significance, what is the critical point for this test? Give your answer to four decimal places.  


D) What is the appropriate conclusion?

a) Fail to reject the claim that W is equal to T because the test statistic is larger than the critical point.

b) Conclude that W is greater than T because the test statistic is larger than the critical point.     

c) Reject the claim that W is greater than T because the test statistic is larger than the critical point.

d) Fail to reject the claim that W is equal to T because the test statistic is less than the critical point.

DATA

Explanation / Answer

A)

"Test to to see if the mean number of crime incidents at Walmart stores is significantly larger", so

OPTION B: b) H0: W = T versus Ha: W > T [ANSWER]

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

b)

The differences are (xW - xT):

-10
-14
-24
43
7
19
11
29
70
41
12
-9
21
-69
-33
7
-4
11
-37
51


Calculating the standard deviation of the differences (third column):              
              
s =    32.92879079          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    7.363101463          
              
Calculating the mean of the differences (third column):              
              
XD =    6.1          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    0.828455241   [ANSWER]

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

c)      
              
As df = n - 1 =    19          
              
Then the critical value of t is              
              
tcrit =    1.729132812   [ANSWER]

*****************************  
              
d)

As t < 1.729, we fail to reject Ho.

OPTION D: d) Fail to reject the claim that W is equal to T because the test statistic is less than the critical point. [ANSWER, D]

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