1. 7-3 Sampling Distribution Models Proportions

2. Qualitative data The normal model of last chapter is applicable to quantitative data.. Remember the formula.

3. Quantitative Data In October of 2004, one poll (of 1016 voters) indicated that 49% of voters would elect John Kerry. A few months later, another poll of 1000 found that 45.9% of voters said that they would choose Kerry. Was one wrong? Is that a big difference? What might a 45.9% media blitz suggest to Kerry supporters? What might a 49% media blitz suggest to Bush supporters?

4. The normal model works The normal model can be applied to proportional situations as well..

5. Sampling Distribution for the proportion ê For the Sampling distribution n = number of trials r = successes p = probability of success q = 1 – p

6. Sampling Distribution for the proportion ê Provided that the sampled values are independent and np and nq > 5, then the random variable can be approximated by a normal random variable x with Call it p hat (not phat) Sample proportion – just like 

7. Huh? Lets try a familiar problem using the Normal model rather than binomial probability… Suppose that about 13% of the population is left handed. A 200 seat lecture hall has been built with 15 lefty sets. In a class of 90 students, what is the probability that there will not be enough sets for the left handed students.

8. Last time We added probabilities above and beyond. The Binomial Model. BUT we can apply the Normal model (why?)

9. Check to see if the normal model applies Are np and nq greater than 5? What are we trying to do? What is ê what is p? What is sd( ê ) n = 90 p =.13; q =.87 Find the probability that more than 15 out of 90 are left handed. If the proportion is typically 13%, what is the probability that more than 16.7% are actually left handed? Where did 16.7 come from?.167.13.035

10. AND…. What we have been doing all along.. Compute the z score and find the area, which is the probability… z score probability 1.06.1446

11. Remember Quantitative data was section 7.2 Qualitative data was section 7.3 Remember to look for samples being independent. Small skewed samples are DANGEROUS

12. At times, remember that: Some books will ask for continuity correction, some will not. Our book does so keep that in mind when doing homework problems. I will try to be very clear when you need to correct.

13. Control Chart Select samples of a fixed size n Regular time intervals r = successes Plot ê in relation to time and look for the out of control signals