1. Inferences About the Population Proportion
Inferences About P
Inferences About the Population Proportion
Each slide has its own narration in an audio file. For the explanation of any slide click on the audio icon to start it.
Professor Friedman's Statistics Course by H & L Friedman is licensed under a  Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 

2. Sampling Distribution of a Proportion
When n*P and n*(1-P) are both ≥ 5, we can use the Z distribution as an approximation to the sampling distribution of the Proportion.
(1-α)% Confidence Interval Estimator of P:
Q: Why does the formula for a CIE use Ps and the formula for Zcalc use P?
Z Test for Proportions

3. Sampling Distribution of a Proportion [Aside]
This formula comes from the fact that the normal distribution can be used to approximate the binomial distribution if np and n(1-p) ≥ 5.
As n gets large and p→.5, then the binomial→normal.
Use when np and n(1-p) 5
Z Test for Proportions

4. EXAMPLE: Did the Politician Lie?
A politician claims that 70% of the people in her district are Democrats. A researcher takes a sample of 100 people and finds that only 50 are Democrats. Is the politician a liar?
(a) Test at α=.05 (2-tail test)
Reject H0 p<.05
Z Test for Proportions

5. EXAMPLE: Did the Politician Lie?
(Continued)
(b) Construct a 2-sided 95% CIE of P
.50  .10
.40 ============ .60
We are 95% confident that the interval .40 to .60 contains the true proportion P of Democrats in the district.
Z Test for Proportions

6. Example: Legalizing Drugs
A politician claims that exactly 90% of the American public favors the legalization of drugs. A survey of 100 people shows that only 79 are in favor of drug legalization.
(a) Test at α=.05
Reject H0 p <.05
Z Test for Proportions

7. Example: Legalizing Drugs
(Continued)
(b) Construct a 2-sided 95% CIE of P
.71 ========= .87
Z Test for Proportions

8. Example: Defective Widgets
A Company claims that no more than 8% of its widgets are defective.
Sample: n = 100; 10 defectives.
Ps = 10/100=.10
Test at α=.05
Construct a 2-sided 95% Confidence Interval Estimator of P.
Z Test for Proportions

9. Example: Defective Widgets
A Company claims that no more than 8% of its widgets are defective.
Sample: n = 100; 10 defectives.
Ps = 10/100=.10
Test at α=.05
Do not reject H0 p > .05
Z Test for Proportions

10. Example: Defective Widgets
(Continued)
(b) Construct a 2-sided 95% CIE of P
.10 ±.06
.04 ======== .16
Z Test for Proportions

11. Homework Practice, practice, practice.
Do lots and lots of problems. You can find these in the online lecture notes and homework assignments.
Z Test for Proportions