AGENDA: DG21 --- 30 min Section 9.2 Register for Mock Exam

Advanced Placement Statistics Section 9.2: Sample Proportions   EQ: How are sample proportions used to estimate population proportions?

RECALL: What are the statistical notations for proportions? Can we really ever know the parameters about a populations? In statistics, we use ESTIMATORS to make decisions about populations. RECALL: What are the statistical notations for proportions?

New Facts: right left

also called Standard Error See Formula Sheet!! also called Standard Error Independence --- Standard Error can be used when n is large enough.

also called Standard Error Standard Error can be used when n is large enough.

Now we can use z-scores!!!

You will need notebook paper for these examples. I would suggest turning your desk so you can work in a SMALL group as we go over these problems. We will work many example problems for the remainder of the course and it will “ take a village” to complete these tasks. In Class Assignment: p. 588 #19 , 20 , 21 You will need notebook paper for these examples.

#19 a) p = true proportion of all US adults who say they drink the milk from their cereal bowl. population > 10(sample) population > 10(1012) population > 10,120 Population large enough for independence. np > 10 nq > 10 (1012)(.7) > 10 (1012)(.3) > 10 708.4 > 10 303.6 > 10 Normal Approximation appropriate.

Since only 1.86% of the samples of size n = 1012 will have 67% or fewer adults saying they drink the milk from their cereal bowl, I would consider these results unusual.

You will need a sample size of 4048 adults to half the standard error. f) If the pollsters had surveyed 1012 teenagers instead of adults , the proportion who say they drink the milk in their cereal bowls would probably be higher. Teenagers are more likely to drink the milk in their bowl.

AGENDA: Need to Finish p. 588 #20 , #21 DG22 --- 20 minutes

#20 a) p = true proportion of all adults who attended church last week population > 10(sample) all adults > 10(1785) all adults > 17,850 Population large enough for independence. (SE) np > 10 nq > 10 (1785)(.4) > 10 (1785)(.6) > 10 714 > 10 1071 > 10 Normal Approximation appropriate.

#21 Problem: What is the probability that a SRS of size n = 300, is within ± .03 of the true population parameter, p = 0.4? population > 10(sample) all adults > 10(300) all adults > 3,000 Population large enough for independence.(SE) np > 10 nq > 10 (300)(.4) > 10 (300)(.6) > 10 120 > 10 180 > 10 Normal Approximation appropriate.

#21 Problem: What is the probability that a SRS of size n = 1200 is within ± .03 of the true population parameter, p = 0.4? population > 10(sample) all adults > 10(1200) all adults > 120,000 Population large enough for independence. np > 10 nq > 10 (1200)(.4) > 10 (1200)(.6) > 10 480 > 10 720 > 10 Normal Approximation appropriate.

The probability that an SRS of adults of size n = 1200 has 37% to 43% who say they attend church regularly is 96.68%.

#21 Problem: What is the probability that a SRS of size n = 4800 is within ± .03 of the true population parameter, p = 0.4? population > 10(sample) all adults > 10(4800) all adults > 480,000 Population large enough for independence. np > 10 nq > 10 (4800)(.4) > 10 (4800)(.6) > 10 1920 > 10 2880 > 10 Normal Approximation appropriate.

The probability that an SRS of adults of size n = 4800 has 37% to 43% who say they attend church regularly is 99.99%.

Assignment p. 589 – 591 #25, 26, 27 (a, b), 28 – 30