Chapter 18: Sampling Distribution Models
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1 Chapter 18: Sampling Distribution Models Key Vocabulary: parameter statistic proportion sampling distribution model Central Limit Theorem Standard error 1. Explain the difference between a parameter and a statistic. 2. Explain the difference between p and ˆp? 3. What is meant by sampling variability? 4. What is meant by the sampling distribution model of a statistic? 5. How is the size of a sample related to the spread of the sampling distribution? 6. In an SRS of size n, what is true about the sampling distribution of ˆp when the sample size n increases? 7. In an SRS of size n, what is the mean of the sampling distribution of ˆp? 8. In an SRS of size n, what is the standard deviation of the sampling distribution of ˆp? Chapter 18: Sampling Distribution Models
2 9. What happens to the standard deviation of ˆp as the sample size n increases? 10. When does the formula pq n apply to the standard deviation of ˆp? 11. When the sample size n is large, the sampling distribution of ˆp is approximately normal. What test can you use to determine if the sample is large enough to assume that the sampling distribution is approximately normal? 12. The mean and standard deviation of a population are parameters. What symbols are used to represent these parameters? 13. The mean and standard deviation of a sample are statistics. What symbols are used to represent these statistics? 14. Because averages are less variable than individual outcomes, what is true about the standard deviation of the sampling distribution of x? 15. What is the mean of the sampling distribution of x, if x is the mean of an SRS of size n drawn from a large population with mean and standard deviation? 16. What is the standard deviation of the sampling distribution of x, if x is the mean of an SRS of size n drawn from a large population with mean and standard deviation? Chapter 18: Sampling Distribution Models
3 17. To cut the standard deviation of x in half, you must take a sample times as large. 18. When should you use to calculate the standard deviation of x? n 19. If is not known, what can you use to estimate the standard deviation of x? What is this called? 20. What does the central limit theorem say about the shape of the sampling distribution of x? 21. What does the law of large numbers state? Chapter 18: Sampling Distribution Models
4 Chapter 19: Confidence Intervals for Proportions Key Vocabulary: standard error confidence level confidence interval margin of error critical value one-proportion z-interval Calculator Skills: 1-PropZInt 1. Describe the sampling distribution model of ˆp. What assumptions must you make for this description to be reasonable? 2. What is the standard error of ˆp? When would you use standard error in place of standard deviation? 3. Explain the meaning of the following statement: We are 95% confident that between 42.1% and 61.7% of sea fans are infected. 4. What is meant by a confidence interval? 5. What is the general form of a confidence interval for a one-proportion z-interval? Chapter 19: Confidence Intervals for Proportions
5 6. Explain how to calculate margin of error. 7. As the confidence level increases, what happens to the margin of error? What happens to the confidence interval? 8. By how many times must the sample size n increase in order to cut the margin of error in half? 9. Why is it best to have high confidence and a small margin of error? 10. What is the critical value z * for a 90% confidence interval? Draw a sketch. 11. What is the critical value z * for a 95% confidence interval? Draw a sketch. 12. What is the critical value z * for a 99% confidence interval? Draw a sketch. Chapter 19: Confidence Intervals for Proportions
6 13. What assumptions and conditions must you consider before creating a confidence interval for a proportion? 14. What effect does increasing your sample size have on the margin of error? What effect does it have on the confidence level? What effect does it have on the confidence interval? 15. The formula used to determine the sample size n that will yield a confidence interval for a ˆˆ population proportion with a specified margin of error m is m z* pq. Solve for n. n Chapter 19: Confidence Intervals for Proportions
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