Question

2. To compare prices of two grocery stores in Toronto, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of July 2018: (12 Points)

Item	Store A	Store B	Difference (Store A - Store B)
1	1.65	1.98	-0.33
2	8.70	8.49	0.21
3	0.75	0.89	-0.14
4	1.05	0.99	0.06
5	11.30	11.99	-0.69
6	7.70	7.99	-0.29
7	6.55	6.99	-0.44
8	3.70	3.59	0.11
9	8.60	8.99	-0.39
10	3.90	4.29	-0.39

1. What are the null and alternative hypothesis if we want to confirm that on average, prices at Store 1 is different from the prices at Store 2, that is, the difference is different from 0?
2. What are the sample mean difference in prices and the sample standard deviation?
3. Compute the test statistic t used to test the hypothesis.
4. Compute the degree of freedom for the test statistic t.
5. Can we conclude that on average, prices at Store 1 is different from the prices at Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
6. Use the above data to construct a 95% confidence interval for the difference in prices between the two stores.
   

Answer 1