Calculate the value of the test statistic. (Do not round intermediate calculatio

Question

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

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

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 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 and s2= 1.95.

Explanation / Answer

Test Statistic
X(Mean)=110.35
Standard Deviation(s.d1)=1.09 ; Number(n1)=10
Y(Mean)=111.21
Standard Deviation(s.d2)=1.95; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =110.35-111.21/Sqrt((1.1881/10)+(3.8025/10))
to =-1.217
| to | =1.217

AT 0.05 LOS

Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 2.262

AT 0.01 LOS

Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 3.25

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