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⎯⎯⎯⎯?=?$124.31x1¯?=?$124.31 and s₁= 1.23. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2⎯⎯⎯⎯?=?$106.18x2¯?=?$106.18 and s₂= 1.63.

(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?

	Fail to reject
	Reject

Answer 1

here, we will do independent 2 sample t test.

hypothesis:-

where, and are population mean shopping expenses of Miller’s and Albert’s store respectively.

given data are:-

A.the test statistic be:-

the degrees of freedom be:-

B).for confidence level 95% the critical value be:-

[ from t distribution table for df = 16,both tailed test, 0.05 level of significance]

C).decision:-

so, the research firm  will reject the null hypothesis.

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