1. Inferences for Population Proportions
Chapter 12
Inferences for
Population Proportions
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2. Definition 12.1 P is fixed P hat is variable depending on sample
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3. Formula 12.1 X is called the number of successes
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4. Key Fact 12.1
If p = .5 then normal approximation is accurate for moderate samples
If far from .5 then we need a bigger n
ROT – np an n(1-p) >5 we can use the normal approximation
we call this “n is large”
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5. = p = 0.191 and standard deviation
Example 12.2
Suppose that 19.1% of all U.S. employees play hooky; that is, that the population proportion is = Then, according to Key Fact 12.1, for samples of size 1010, the variable is approximately normally distributed with mean
= p = and standard deviation
Use simulation to make that fact plausible.
Change to page 745
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6. Solution Example 12.2
We first simulated 2000 samples of 1010 U.S. employees each. Then, for each of those 2000 samples, we determined the sample proportion, , of those who play hooky. Output 12.1 shows a histogram of those 2000 values of , which is shaped like the superimposed normal curve with parameters and
Output 12.1
Change to page 745
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7. Procedure 12.1 Common z alphas are in table IV Example 12.3
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8. Definition 12.2 This is the +/- n-sigma from before
Usually a 95% confidence interval
We see this in political polling
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9. Formula 12.2 This is solving E for n
.25 comes from the largest p(1-p) which is most conservative.
Example 12.2
HW 12.13, 14, 16 by hand and minitab
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10. Procedure 12.2 Similar to before
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11. Procedure 12.2 (cont.) Example 12.6
HW 12.50, 53, 58 By hand and minitab.
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12. Homework 12.13, 14, 17, 18, 20, 21 by hand and minitab
Example 12.6
HW 12.50, 53, 58 By hand and minitab.
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