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

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.

Assignment 8q5 data:

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?

H0: W = T versus Ha: W TH0: W = T versus Ha: W < T    H0: W = T versus Ha: W > TH0: 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?

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

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

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

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

Walmart Target 896 844 585 624 493 458 813 691 955 1008 876 832 694 616 644 606 670 622 941 906 833 837 1021 957 816 768 862 777 831 862 876 851 740 747 1042 1037 831 781 892 807

Explanation / Answer

(a) Here Hypothesises are :

H0 : W = T

Ha : W > T

(b) The test used here is t - test for two paired means

Average of difference dbar = 34

standard deviation of difference between crime at walmart stores and Target stores sd = 44.7461

Test statistic

t = dbar/ (sd / sqrt(n)) = 34/ (44.7461/ sqrt(20) =  3.3981

(c) Alpha = 0.05  

dF = 20 -1 = 19

critical test statistic

t38,0.05 = 1.7291

(d) Here t > tcritical so we shall reject the null hypothesis and concludeFail to reject the claim that W is equal to T because the test statistic is larger than the critical point. Option C is correct.

Walmart Target Difference 896 844 52 585 624 -39 493 458 35 813 691 122 955 1008 -53 876 832 44 694 616 78 644 606 38 670 622 48 941 906 35 833 837 -4 1021 957 64 816 768 48 862 777 85 831 862 -31 876 851 25 740 747 -7 1042 1037 5 831 781 50 892 807 85 Average 34 Std. Dev. 44.7461

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