Question

A young statistics professor upon getting his first teaching job and moving to a new community told his wife he would compare the prices at the two grocery stores closest to their new house. As an experiment he made a list of a sample of 25 items that they typically purchased as part of their regular grocery shopping. He then visited both stores and recorded the price for the items at each store. The data appears below. Is there evidence of a difference in the mean price between the two stores? Test using a .05 level of significance.

Item Store1 Store2

1    6.90    5.90

2    4.50    4.20

3    3.10    2.00

4    5.90    6.20

5    3.60    2.50

6    3.40    3.00

7    5.30    5.60

8    7.00    6.20

9    2.40    2.50

10    7.00    7.50

11    4.90    4.00

12    3.10    2.60

13    4.16    3.65

14    4.71    4.53

15    5.56    5.47

16    6.59    5.35

17    3.92    3.59

18    6.94    6.59

19    5.89    5.28

20    6.26    5.63

21    1.75    1.65

22    6.53    5.74

23    1.56    1.83

24    7.15    6.72

25    6.09    5.94

Answer 1

Null Hypothesis: There is no difference in the mean price between the two stores i.e., they are independent

Alternative Hypothesis: There is a difference in the mean price between the two stores i.e., they are not independent

From.the below table the P- value is 0.417 which is greater than 0.05. So, there is no evidence to reject the null hypothesis. Hence we can conclude that there is no difference in the mean price between the two stores i.e, they are independent