4. Inferences about the difference between two population means Matched samples

Question

4. Inferences about the difference between two population means Matched samples Aaa Aa Are store brand grocery items actually cheaper than their name-brand counterparts? A data set constructed by Michael McKay, a business statistics student at Fairfield University, will help you answer this question Michael collected data on the prices of store-brand and name-brand items sold at Groceries Plus (not its real name) To select his sample, he made a preliminary visit to Groceries Plus to study the layout of the store. Then he used a random-number generator to select a series of four random numbers. The first random number provided an aisle number, the second random number provided a distance into the aisle, the third (0 or 1 indicated the shelf on the right or the left side of the aisle, and the fourth provided a shelf number. The store-brand item that was located nearest to the position dictated by the set of four random numbers was pulled into his sample You will work with a sample of grocery items that was randomly selected from Michael's data set. The sample data are shown in the DataView tool that follows Data Set Groceries Sample Variables 3 Observations 12 Store-Brand and Name-Brand Prices for a Sample of Grocery Store ltems Sample data collected by Michael McKay, business stats student, Fairfield University Variables Observations Observations Variable v Type v Form Values v Missing v Quantitative Numeric 12 Name-Brand Price Quantitative Numeric 12 Store-Brand Price Quantitative Numeric 12 Difference in Price Variable Variable Variable Correlation Correlation Which of the following statements best describes how the data were collected and how they should be analyzed to make inferences about Hd, the mean difference in price between name-brand and store-brand items sold at Groceries Plus? O Collected two independent samples of size 24 each; analyze two samples of 12 differences each O Collected a single sample of 12 pairs of data values; analyze a single sample of 24 differences O Collected a single sample of 12 pairs of data values; analyze a single sample of 12 differences O Collected two independent samples of size 12 each; analyze a single sample of 12 differences

Explanation / Answer

For question 1 . Option C  is correct , collected a single sample of 12 pairs of data values,; analyse a single sample of 12 differences.

Explaination : Option A and Option D is for independent samples, so it is wrong.Similarly, Option B creates 24 differences, it is not possible to create it from 12 paired samples. so option C is correct.

FOr question 2. Hypothesis test is

H0 : d $ 1.25, that means the differences between name - brand prices and store- brand prices, which also means savings is more than $1.25, which is shown in advertisement.

Ha : d < $ 1.25,that means the differences between name - brand prices and store- brand prices, which also means savings isess than $1.25, which is against what is shown in advertisement.

Q.3 The p - value is 0.75. You reject the null hypothesis, because the p- value is greater than the level of significance. Therefore, you reject tand conclude that the grocery store's claim is false.

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