lect15v4_1up

lect15v4_1up - Stat 104: Quantitative Methods for...

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Stat 104: Quantitative Methods for Economists Class 15: Sampling and the Central Limit Theorem 1
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You Could be Wrong s Have you ever not completed a task fully? s Suppose you’re a teacher’s aid at school, and for a state mandated school audit, you need to find the average weight of all 500 students at the school. In an effort to save time and hassle, you decide to simply query the first 30 people you see at lunch, and report the resulting sample average as the population value. s How wrong could you be? 2
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You Could be Wrong s Quality control at Office Depot is very important, particularly when it comes to their own private label products. s On the average, 500-foot rolls of transparent tape should be close to the specified length. In evaluating a hipment from their supplier, ffice Depot kes a shipment from their supplier, Office Depot takes a random sample of 100 rolls of tape, and the mean length of the sample is determined. s If the mean is greater than 490 feet, the entire shipment is accepted; otherwise, the shipment is rejected and sent back to the manufacturer. What’s the risk of Box Depot accepting a shipment of inferior tapes? 3
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We’re Wrong-How Wrong Are We? s The common theme is “you could be wrong”. s That is, there is no guarantee when using sample data that a correct decision will be made. s Your thinking should always be, “I could be wrong. Let’s uantify how wrong I could be.” quantify how wrong I could be.” s This class begins our foray into statistical inference, which is simply the study of how to generalize from a sample to a population, from the specific to the general. s It should be noted that this is a “big ideas” class, in which a very important theoretical result, possibly the most important one in statistics, is presented. 4
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Motivating Example s Suppose you are a reporter for your college newspaper, and are interested in how much time your fellow students spend on facebook.com each week. here re round 0 00 ndergraduates t our s There are around 10,000 undergraduates at your college, so asking each of them how much time they spend on facebook during a typical week doesn’t seem that feasible. s Instead, you do what numerous reporters and researchers before you have done and take a random sample . 5
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The Random Sample s A random sample is simply a selection from a population of interest where everyone in the population has an equal chance of being selected. b A relevant population needs to be defined and established. For
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lect15v4_1up - Stat 104: Quantitative Methods for...

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