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Unformatted text preview: 139-Spring 09 Midterm 1Name ..................................................................February 12, 2009Notes:1. Use a calculator where necessary2. Show your working.3. Make use of the cheat sheet and the additional formulae posted below.4. If you want to make any additional assumptions, please state them clearly.5.Keep verbal answers concise(no more than 3 sentences, and bullet points are &ne).5. There are 75 points in total (1 point per minute)6. The questions are intended to be done sequentially.7. Place your answers in the spaces provided.The blank pages at the back are intended to beused as scratch.Background:The questions in this exam are motivated by "scanner" datasets which containinformation collected from checkout scanners in supermarkets. The typical scanner dataset containssales data on a number of speci&c products from a large sample of supermarkets in large US cities.Duke has one of these datasets which is potentially available for undergraduate research projects. Thequestions below are based on data for large multipacks (288 oz.) of regular Pepsi in 2005.Useful formulae:if W is Bernoulli random variable, equal to 1 with probabilityq(0 otherwise),thenE(W) =qandV ar(W) =q(1&q).DO NOT TURN OVER UNTIL TOLD TO DO SO11. [16 points] Two of the variables in the data are indicators (i.e., they are equal to zero or one).SALEis equal to one if the price in the store is below the regular store price in a given week and zerootherwise; andADVERTis equal to one if the product is advertised by the store in a given week (e.g.,mentioned in a &yer distributed to consumers) and zero otherwise. The number of store-weeks whenthe item is on sale and/or being advertised are given in the following table.SALE= 0SALE= 1TotalsADV ERT= 010,3514,45414,805ADV ERT= 111,69815,69827,396Totals22,04920,15242,201(a)(i) [2 points] Calculate the proportion of store-weeks when Pepsi is on sale....
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- Spring '08