Question

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1⎯⎯⎯⎯?=?$110.35x1¯?=?$110.35  and s₁= 1.09. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2⎯⎯⎯⎯?=?$111.21x2¯?=?$111.21 and s₂= 1.95.

(a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Test statistic            

(b) Calculate the critical value. (Round your answer to 2 decimal places.)

Critical value            

Answer 1

Solution:

We use t-test for difference of means in order to compare prices charged by two supermarket chains—Miller’s and Albert’s.

n1=n2=10 , x1= $110.35 and s1= 1.09, x2=111.21 and s2= 1.95

i) Test statistic

t = 110.35- 111.21/ √ ((1.09) ^2 + (1.95) ^2) / 10

t= -0. 86/0.7064 = -1. 22

ii) Critical value

t at n1+n2-2 d. f = t at 18 d. F for 0.05 level of significance is

T-Value (right-tailed): 1.734064= 1.73

T-Value (two-tailed): +/- 2.100922= 2.10