Question

In: Statistics and Probability

A consumer group wished to compare the price of food items at two supermarkets A and...

  1. 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

Solutions

Expert Solution

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.


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