Chapter 18
Inference about a Population Proportion
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 The sample proportion
 The sampling distribution of
 Conditions for inference
 Large-sample confidence intervals for a population proportion
 Choosing the sample size
 Significance tests for a proportion
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1. The Sample proportion p
ˆ
 The proportion of a population that has some outcome (“ success ”) is p .
 The proportion of successes in a sample is measured by the sample proportion :
 count of successes in the sample total count of observatio ns in the sample
“ phat”
3

2. The sampling distribution of p
ˆ
4

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3. Conditions for inference
6

Standard Error of
Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be
ˆ p .
s.d.
 p(1 p)

 s .
e .
 n n
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4. Large-sample confidence intervals for a population proportion
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 Example 18.4 Estimating risky behavior
(Page 476)
 Example 18.5 Are the conditions met?
(Page 476)
 Exercise 18.8 No confidence interval.
(Page 477)
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5. Accurate C.I. for a proportion
 Example 18.6 (P479) Shaq’s free shows
10

 The margin of error in our confidence interval is m
 z *
( 1

) n
 We may like to choose the sample size n to achieve a certain margin of error.
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Guess the sample proportion:
 Since we don’t know prior to sampling, we will have to use a guess p* for . There are two ways to do this:
– Use a guess p* based on a pilot study or on past experience.
– Use p*=0.50 as the guess. This guess is conservative, as it gives a margin of error bigger than the true margin of error. (Conservative)
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 Example 18.7 Planning a poll
(Page 482)
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7. Significance tests for a proportion
15

 Example 18.8 Is this coin fair?
(Page 484)
 Example 18.9 Estimating the chance of head (Page 485)
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