Chance Errors in Sampling (Dr. Monticino)

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Presentation transcript:

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

Assignment Sheet Read Chapter 20 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

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

Central Limit Theorem: Averages 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

Examples 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?

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…

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) SE without replacement =  SE with replacement