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# l8 - Math 127B Notes for lecture 8 Mrinal Raghupathi...

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Math 127B, Notes for lecture 8 Mrinal Raghupathi Wednesday, February 9th, 2011 Administrivia The topics to be discussed today are weighting, half-samples and probability samples. The material is based on chapter 22. Reminders 1. Read chapter 23.1 – 23.2 for Monday. There is an online quiz posted due by Monday 8 am. 2. Homework 4 is due Thursday, 2/10 in recitation. 3. There will be a quiz in recitation over chapter 21. 1 Weighting the sample A survey of undergrads is conducted to ﬁnd out how the average number of credit hours taken by undergraduates each semester. A sample of 100 undergraduates reveals the following ﬁgures Credit hours Class Number Average Total Senior 21 12 12 × 21 = 252 Junior 28 14 14 × 28 = 392 Sophomore 26 13 13 × 26 = 338 Freshmen 25 15 15 × 25 = 375 The university registrar informs us each of the four classes has an equal representation in the university and from this we see that the seniors are under-represented in our sample. To compensate for this we will assign a weight to each group. What is a weight? A weight is a number that we will assign to each group that will compensate for their size relative to the population. A weight of 1 should be assigned to a group that has a size 1

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equal to its proportion in the population. Under-represented groups should be assigned weights larger than 1. A simple way to get a weight is to compare the ratio of the size of the group in
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l8 - Math 127B Notes for lecture 8 Mrinal Raghupathi...

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