1. Ch 12 – Inference for Proportions YMS 12.1
Inference for a Population Proportion

2. Ch 9 Sampling Distributions
is an unbiased estimator of population proportion p
Standard deviation of is if the population is at least 10 times n
Sampling distribution of is approximately normal if np and n(1-p) are at least 10
Use z-scores to standardize

3. Conditions for Inference
To be representative: Data are from an SRS from the population of interest
To accurately calculate standard deviation: Population is at least 10 times n
To use normal calculations: Counts of successes/failures must be at least 10

4. Test of Significance Ho: p = po
Standard Error
Replacing p with in standard deviation formula
Test of Significance Ho: p = po
Verify that npo and n(1-po) are at least 10
Formula
Confidence Interval
Verify that n and n(1- ) are at least 10
Form

5. Choosing the Sample Size
Margin of error
Use a guess for p*
Based on previous data
Use the conservative estimate of 0.5 (unless you believe is closer to 0 or 1 because then p* = 0.5 will give you a much larger sample size than necessary)

6. Which to use in formulas and conditions?
Hypothesis Tests
Use po because that is the distribution you’re comparing your result to
Confidence Intervals
Use because you don’t have any other values (remember you’re using the CI to estimate the true proportion p)
p698 # , 12.17

7. Comparing Two Proportions
YMS 12.2
Comparing Two Proportions

8. Sampling Distribution of
When samples are large, the sampling distribution is approximately normal.
Mean
Variance

9. Confidence Intervals for Comparing Two Proportions
Same form as for two means and standard error is replacing p with
Conditions are still SRS, a population at least 10 times n, but now n1 , n1(1- ), n2 , and n2( ) are all greater than 5
p706 #

10. Pooled Sample Proportion
Because both samples actually come from one huge population, we combine the sample results to estimate the unknown population proportion p
Formula

11. Significance Tests for Two Props
Replace and with pooled in standard error formula and the conditions for count of successes and failures
Other conditions remain the same!
Test Stat
p707 #
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