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Chance Errors in Sampling (Dr. Monticino)

0. Chance Errors in Sampling (Dr. Monticino). Assignment Sheet. 0. Read Chapter 20 Assignment # 13 ( Due Wed. April 27 th ) Chapter 20 Exercise set A: 2,3,4; Exercise set B: 1,2,3 Exercise set C: 2,3,4. Overview. 0. Review Central Limit Theorem for averages (percentages) Examples

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Chance Errors in Sampling (Dr. Monticino)

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  1. 0 Chance Errors in Sampling(Dr. Monticino)

  2. Assignment Sheet 0 • Read Chapter 20 • Assignment # 13 (Due Wed. April 27th) • Chapter 20 • Exercise set A: 2,3,4; • Exercise set B: 1,2,3 • Exercise set C: 2,3,4

  3. Overview 0 • Review Central Limit Theorem for averages (percentages) • Examples • Correction factor when sampling without replacement

  4. Central Limit Theorem: Averages 0 • For a large number of random draws, with replacement, the distribution of the average = (sum)/N approximately follows the normal distribution • The mean for this normal distribution is • (expected value for one repetition) • The SD for the average (SE) is • This holds even if the underlying population is not normally distributed

  5. Examples 0 • Suppose that 25% of likely voters are undecided on who they will vote for in the upcoming presidential election. 400 eligible voters are selected at random • What is the expected number of people in the sample that will be undecided? • What is the expected percentage of people in the sample that will be undecided? • What is the SE for the number of people in the sample that will be undecided? • What is the SE for the percentage of people in the sample that will be undecided? • What is the probability that between 70 and 90 people in the sample will be undecided • What is the probability that between 18% and 22% of the people in the sample will be undecided • Between what two values (centered on the expected percentage) will 95% (99%) of the sample percentages lie?

  6. Accuracy of Percentages • The accuracy of the sample percentage is determined by the absolute size of the sample, not the size relative to the population • Example…

  7. SE without replacement =  SE with replacement Correction Factor • If the sample is selected from the population without replacement and the sample is large with respect to the population, then a correction factor is needed for the standard error • “When the number of tickets in the box (population) is large relative to the number of draws (sample), the correction factor is nearly 1 and can be ignored.” (Dr. Monticino)

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