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Mid1nosol - 139-Spring 09 Midterm 1 Name Notes 1 Use a...

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139-Spring 09 Midterm 1 Name .................................................................. February 12, 2009 Notes: 1. Use a calculator where necessary 2. 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 be used as scratch. Background: The questions in this exam are motivated by "scanner" datasets which contain information collected from checkout scanners in supermarkets. The typical scanner dataset contains sales 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. The questions 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 probability q (0 otherwise), then E ( W ) = q and V ar ( W ) = q (1 ° q ) . DO NOT TURN OVER UNTIL TOLD TO DO SO 1
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1. [16 points] Two of the variables in the data are indicators (i.e., they are equal to zero or one). SALE is equal to one if the price in the store is below the regular store price in a given week and zero otherwise; and ADVERT is 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 when the item is on sale and/or being advertised are given in the following table. SALE = 0 SALE = 1 Totals ADV ERT = 0 10,351 4,454 14,805 ADV ERT = 1 11,698 15,698 27,396 Totals 22,049 20,152 42,201 (a)(i) [2 points] Calculate the proportion of store-weeks when Pepsi is on sale.
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