Green Foods Grocery Inc has two grocery stores located in Oc

Green Foods Grocery Inc. has two grocery stores located in Ocean City. One store is located on 1st Street and the other on 41st Street and each is run by a different store manager. Each manager claims that his store\'s layout makes the most of customers. Both managers conducted surveys on a sample of their customers and asked them how much more they spent than they had planned to because of store’s layout? The following table shows the sample data collected from the two stores. Upper management at Green Foods Grocery Inc. wants to know if there is a difference in the mean amounts purchased at the two stores and has hired you to perform the statistical analysis.

1st Street/ 15.78 | 17.73 | 10.61 | 15.79 | 14.22 | 13.82 | 13.45 | 12.86 | 10.82 | 12.85

41st Street/ 15.19 | 18.22 | 15.38 | 15.96 | 21.92 | 12.87 | 12.47 | 13.96 | 13.79 | 13.74 | 18.4 | 18.57 | 17.79 |10.83

Solution

Sample 1: 15.78 , 17.73 , 10.61 , 15.79 , 14.22 , 13.82 , 13.45 , 12.86 , 10.82 , 12.85

Mean =13.79 , n=10

SD = 2.22

Sample 2 : 15.19 , 18.22 , 15.38 , 15.96 , 21.92 , 12.87 , 12.47 , 13.96 , 13.79 , 13.74 , 18.4 , 18.57 , 17.79,10.83

Mean =15.65 , n=14

SD = 3.01

z = [ (x₁ - x₂) - d ] / SE

SE =sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

Therefore ,

z = (( 13.79 -15.65 ) -0 ) / sqrt (((2.22)²/10) + ((3.01)²/14)))

= -1.74

P-value = 0.409 + 0.409 = 0.818 Answer    [ Two tailed test]

Hence , failed to reject null hypothesis.