12­5 Samples 2011 February 18, 2011
Warm ­ up
Find the following given the data set:
21, 22, 27, 12, 22
a) Mean
b) Standard Deviation
c) Find the z­score when the value is 17
d) Find the value that has a z­score of about 1.15
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12­5 Samples 2011 February 18, 2011
12­5
Working with
Samples
Objectives: To calculate sample proportions and margins
of error.
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12­5 Samples 2011 February 18, 2011
Suppose you want to find out what percent
of people watch American Idol.
Since it is not practical to collect data on an
entire population we use a smaller
proportion, or a sample.
This data from the sample reflects the data
of the entire population.
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12­5 Samples 2011 February 18, 2011
Definitions
Sample: Part of a population. Gathers information from any part
of a population.
x
Sample Proportion: The ratio
n where x is the number of times
an event occurs and n is the sample size
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Margin of Error
Each sample proportion should be reported with a margin of error ­ an
estimate of error.
The margin of error is based on the standard deviation.
The larger the sample size, n, of a proportion, the smaller the margin of
error.
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Estimate the sample size for each margin of error:
_ 10%
1. +
_ 4%
2. +
_ 2%
3. +
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12­5 Samples 2011 February 18, 2011
Example 6: In a survey of 380 art students
32% reported that their favorite color is red.
a) Find the margin of error for the sample.
b) Find an interval that is likely to contain the true population
proportion.
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Homework
12­5
Pg. 680 # 1­3, 9­19
odd, 22, 26, 28
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