Sampling Distributions: Proportions

1. Sampling Distributions: Proportions

3. Sampling Reese’s Pieces

5. http://www.rossmanchance.com/applets/Reeses3/ReesesPieces.htmlhttp://www.rossmanchance.com/applets/Reeses3/ReesesPieces.html

6. Sampling Distribution of Proportions The distribution of the sample proportions computed for all possible samples of a given size drawn from a population is called the (theoretical) sampling distribution of the sample proportions. These simulated sample proportions approximate the theoretical sampling distribution. Increasing the number of samples in the simulation improves the approximation and helps us discern the long-term pattern of the results (i.e., the distribution and its variability)

7. Central Limit Theorem (CLT) for a Sample Proportion Suppose a simple random sample of size n is selected from any large population (more than 10 times as large as the sample) having a true proportion equal toπ. Then we can predict three things about the sampling distribution of the sample proportion p-hat: Shape: The distribution will be approximately Normal. Center: Its mean will equal π. Spread: Its standard deviation will equal sqrt[π(1-π)/n] This Normal approximation becomes increasingly accurate as the sample size n increases and is generally considered to be valid provided that two conditions are met: nπ ≥ 10 AND n(1-π) ≥ 10.

8. Watch Out!!

9. Watch Out!!

10. Watch Out!! nπ ≥ 10 AND n(1-π) ≥ 10

11. Watch Out!!