Question

11. A consumer group wished to compare the price of food items at two supermarkets A and B. A random sample of 8 items was selected and the cost of the items at each supermarket was recorded on a particular day.

Item 1 2 3 4 5 6 7 8

A $3.60 $3.73 $3.48 $2.43 $2.81 $2.66 $3.62 $2.40

B $3.38 $3.77 $3.50 $2.55 $2.82 $2.65 $3.74 $2.31

(a) test at α = .05 if "on average" the prices offered at the two supermarkets differ. (d= .0013, sd = .1118)

(b) Conduct the test in (a) using appropriate confidence interval

Answer 1

Number	A	B	Difference
	3.6	3.38	0.22	0.04785156
	3.73	3.77	-0.04	0.00170156
	3.48	3.5	-0.02	0.00045156
	2.43	2.55	-0.12	0.01470156
	2.81	2.82	-0.01	0.00012656
	2.66	2.65	0.01	7.6563E-05
	3.62	3.74	-0.12	0.01470156
	2.4	2.31	0.09	0.00787656
Total	24.73	24.72	0.01	0.0874875

To Test :-

H0 :-  

H1 :-

Test   Statistic :-





t = 0.0316

Test   Criteria :-
Reject   null hypothesis if  


Result :-    Fail to reject null hypothesis

Confidence Interval :-



Lower Limit =
Lower Limit = -0.0924
Upper Limit =
Upper Limit = 0.0949
95% Confidence interval is ( -0.0924 , 0.0949 )

Since 0 lies in the interval, we can conclude to accept null hypothesis

Conclusion :- There is no sufficient evidence to conclude that the average prices offered at the two supermarkets differ.