A marketing research firm wishes to compare the prices charged by two supermarke

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 x_1 = exist121.92 and s_1 = 1.40. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert's stores are x^2 = exist114.81 and s_2 = 1.84. Assuming normality, test to see if the corresponding population standard deviations differ by setting alpha equal to 05. Is it reasonable to use the equal variances procedure to compare population means? (a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic 1.73 (b) Calculate the critical value. (Round your answer to 2 decimal places.) Critical value 3.18 (c) At the 0.05 significance level, what it the conclusion? Reject H_0 Fail to reject H_0

Explanation / Answer

Here we need to use F-test for variances:

F = s1^2/s2^2

   = 1.84^2/1.40^2

   = 1.73

Test Statistics =1.73

Critical F formula using excel

=FINV(0.025,10-1,10-1)

=4.03

Critical value = 4.03

Test value is less than the critical value

Fail to reject Ho

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