l15 - Math 127B Notes for lecture 15 Mrinal Raghupathi...

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Math 127B, Notes for lecture 15 Mrinal Raghupathi Monday March 21st, 2011 Administrivia Today we will discuss the χ 2 goodness-of-fit. Reminders 1. Homework 8 is due Thursday, 3/24 in recitation. 2. Quiz in recitation over chapter 27 on 3/24. 3. This week’s recitation will be a discussion of problems from chapter 28. 1 The χ 2 -test The χ 2 -test helps us to decide whether a collection of observations fits a given model or a list of frequencies. Example 1 . A die is rolled 60 times. The observed frequencies are shown below. A fair die would land on each value about one-sixth of the time, or about 10 times each. It is highly unlikely that a die will show each number exactly 10 times. (The chance is about 1 in 13,000). The question is whether the observed differences are due to chance or are real. Face Observed Expected 1 11 10 2 13 10 3 15 10 4 10 10 5 9 10 6 2 10 One way to determine this is to use the z -test. The 60 rolls of the die are like 60 draws with replacement from the box 1
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l15 - Math 127B Notes for lecture 15 Mrinal Raghupathi...

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