9. Inference about the difference between two means - Matched pairs experiment 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 randomly selected a sample of products and then collected data on the prices of the store-brand and the name-brand items sold at Groceries Plus (not its real name). For each selected grocery item in Michael's sample, the name-brand price, the store-brand price, and the difference in those prices (name-brand minus store-brand) are shown in the DataView tool that follows. Data Set Groceries Sample Variables = 3 Observations = 10 Store-Brand and Name-Brand Prices for a Sample of Grocery Store Items Sample data collected by Michael Mckay, business stats student, Fairfield University Variables Observations Variable V Type V Form Values V Missing Observations Name-Brand Price Quantitative Numeric 10 Store-Brand Price Quantitative Numeric 10 Difference in Price Quantitative Numeric 10 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 UD, the mean difference in price between name-brand and store-brand items sold at Groceries Plus?Cl- Collected a single sample of 10 pairs of data values; analyze a single sample of 20 differences '12:? Collected a single sample of 10 pairs of data values; analyze a single sample of 10 differences Cl Collected two independent samples of size 20 each: analyze two samples of 10 differences each {:3- Collected two independent samples of size 10 each; analyze a single sample of 10 differences Groceries Plus advertises that its store brand provides a savings to its customers of $1.25 per item on average. As a statistics consultant to the Better Business Bureau, you are asked to investigate the grocery store's claim using a hypothesis test. If there is sufcient statistical evidence to infer that the average savings per item is less than $1.25, the Better Business Bureau will take action to have Groceries Plus correct its advertising. The Better Business Bureau requests a 0.10 level of significance for your hypothesis test. (Hint: Dene up = Hmbmlpm Hmwbbmipm such that up 3 0 ifon averagethe name-brand products cost more than the mean store-brand products and up <: if the store-brand products cost more than namebrand products. you conduct v hypothesis test with null and alternative hypotheses formulated as: c:- h4 lid="1.25" :hl: ijd hi on c pd="1.25" hu: pp="1.25">125 Ci:- H4]: LID = 1.25;H1:pD =1.25 Assume that the population of price differences has a normal distribution. The value of the test statistic for the hypothesis test is v . (Hint: Use the DataView tool to find the appropriate sample mean and standard deviation.) Use the Distributions tool to help you answer the questions that follow. Select a Distribution Distributions 0 1 2 3 The p-value is You the null hypothesis because the p-value is than the level of significance a = 0.10. Therefore, you infer that the grocery store's claim is false