1. Chapter 9.1, 9.2 and 9.3 Sampling distribution of means and proportions

2. Vocabulary—use Cornell Notes Parameter– The “parameter of interest” is a description of the population at hand. Men over 40 La Quinta Boys in the freshman class. People who shop at Wal-Mart. Statistic—a sample of the overall parameter that attempts to describe the parameter. Sample of 20 boys from the freshman class randomly selected. Sample people as they leave the checkout at Wal-Mart.

3. Vocabulary Continued Bias—how far off from the parameter your statistic is. (Could have high or low bias) Variability---if you took multiple samples how dispersed are these samples.—see next slides for how it may look.

12. Vocabulary continued P: P is a parameter statistic (also Greek letter Л ) and it is the true population proportion. P-hat: this is the proportion of a statistic involving proportions.

13. Vocabulary Continued μ– this is the mean of a population.—rarely known. X-bar: this is the mean of a sample—X-bar’s goal is to be an estimator of μ. σ –this is the populations’ standard deviation. S– this is the standard deviation of a sample—it is meant to be an unbiased estimator of σ.

14. Activity for 9.1 Flip a coin 10 times and report your proportion of heads. Chart of the distribution of P-hat in this situation. Is P-hat close to the known P of.5? It is assumed that 20% of all Americans will get cancer. Simulate 20 Americans on a random digit table and decide how you will simulate 20%. Then report what proportion of your 20 American’s will get cancer.

15. The point for 9.1!! Here’s the point—if you sample well enough, your mean of your sampling distribution will match exactly the parameter of the population (either P or μ). Take a sample of numbers like 2,4,6,8 and do all possible combinations of size 2. Chart the work. See if the resulting sampling distribution has a mean of 5, which is the mean of those 4 numbers. TRY IT!!

16. 9.2 Sample proportions Let’s sample for a proportion---roll 1 die and tell me the proportion of times you get a 1. Chart the distribution of P-hat. Is the mean of this distribution close to P. What is P in this situation? Some facts about the distribution of P-hat. It’s distribution is close to normal in shape if you have enough samples. It’s mean is close to P It’s standard deviation gets smaller as the sample size gets larger.

17. 9.2 sample proportions The mean of the distribution of p-hat is P (the often unknown parameter) The standard deviation is Sqrt p(1-p)/n There are two rules that you need to know involving proportions. 1. np≥10 and n(1-p)≥10 ---this ensures that there is a big enough sample size for the distribution to be normal. 2. The overall population needs to be 10 times the sample size---this ensures that the issue of replacement is not violated so that the standard deviation will work.

18. Practice 9.2 Do 9.15, 9.17, 9.19, and 9.21 together— assignment number 4.

19. 9.3 sample means Recall the activity at the beginning of the chapter.—Average height of an American female. What was the general rule? The mean x-bar of the sample means should be close to μ. The standard deviation of the distribution of sample means is σ/sqrtof N.

20. Let’s practice There are 200 boys in the freshman class with a mean height of 64” and a standard deviation of 3 inches. Assume that the heights are normally distributed. What is the probability that a randomly chosen boy will be 67 inches tall or more? Same scenario as above. What is the probability that 10 randomly chosen boys will average 67 inches tall or more? What is the mean and standard deviation of 20 kids? Of 50 kids?

21. Practice!! Which question of the previous would be most affected if the data is non-normal? Introduce the central limit theorem.—it is the activity and web-site that we looked at before.

22. Relating sample proportions with sample means and binomials What is the probability of rolling a two die 500 times and getting more than 100 sevens? Do this with a binomial calculation. Remember to cover the requirements (assumptions) Do this with a proportion calculation. Remember to cover the assumptions or requirements. Do this with a means calculation. Remember to cover the requirements.