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l2 - Math 127B Notes for lecture 3 Mrinal Raghupathi Monday...

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Math 127B, Notes for lecture 3 Mrinal Raghupathi Monday, January 24th, 2011 Administrivia The topics to be discussed today are the chance model for inference and chance errors in sampling. Most of the material is taken from chapter 19.8, 20.1, 20.2. Reminders 1. Read chapter 20 by Wednesday. There is an online quiz posted. Details on how to access the quiz were sent by email. 2. Homework 2 is due Thursday, 1/27 in recitation. 3. There will be a quiz in recitation over chapter 19. 1 Chance error in sampling The goal of statistical inference is to make an estimate about the population from a subgroup. The smaller group of people is called the sample. The quantity that we are trying to estimate is called a parameter and the calculation we make for the sample is called the statistic . Example 1 . We want to estimate the average number of credit hours taken by students at Vanderbilt this semester. The population is all Vanderbilt undergraduates. The parameter is the average number of hours. If we were to select a random sample of 100 students and compute the average number of credit hours for the sample, then we would be computing a statistic. There is going to be a difference between the true value of the parameter and the estimate that we make. Part of this error will be a systematic bias that will be the same for all students in the sample. The rest of the difference is down to chance error. Therefore we have the chance model average in the sample = average for all students + bias + chance error o 1
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In general, the chance model is given by estimate = parameter + bias + chance error . We will try to answer the following basic questions: How big is the chance error? How do we control the error? How does the error depend on the sample size and the population size? Before we continue let us come up with a box model for the above example. Let us assume that the current enrollment is 7,000 students. We can imagine a box in which there are 7,000 tickets, one for each student. We can also imagine that each ticket has the number of credit hours the student is taking written on it. The average number of credit hours is the average of the numbers of these tickets and is the average of the box.
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