Math 127B, Notes for lecture 15
Mrinal Raghupathi
Monday March 21st, 2011
Administrivia
Today we will discuss the
χ
2
goodnessofﬁt.
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 onesixth 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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 Spring '11
 Staff
 Math, Statistics, Frequency, Null hypothesis

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