Question

A marketing research firm wishes to compare the prices charged by two supermarket chains-Millers and Alberts. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chains 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 Millers stores are $121.92 and $1.40, respectively. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Alberts stores are $114.81 and $1.84 respectively Assuming normality, test to see if the corresponding poonstandard deviations differ by setting a equao5ale o sethe equal variances procedure to compare population means? 05. I (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 (c) At the 0.05 significance level, what it the conclusion? Reject Ho Fail to reject Ho

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Answer #1

The provided sample varanes ae1.96 and s2 3.3856 and the sample sizes are given by n 10 and n2 10 (1)Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used (2) Rejection Region Based on the information provided, the significance level is α 0.05, and the the rejection region for this two-tailed test is R-F:F<0.248 or F>4.026 The F-statistic is computed as follows s 1.96 F = - 0.579 3.3856 Since from the sample information we get that FL concluded that the null hypothesis is not rejected 0.248 < F 0.579 < Fu4.026, it is then (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance σ1 is different than the population variance σ, at the α 0.05 significance level

A)

TS = 0.579

B)

critical value = 4.026 and 0.248

c)

fail to reject Ho

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