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This 3 page Class Notes was uploaded by Debra Tee on Saturday October 8, 2016. The Class Notes belongs to STATS 250 at University of Michigan taught by Thomas Venable Jr in Fall. Since its upload, it has received 3 views. For similar materials see /class/231658/stats-250-university-of-michigan in Statistics at University of Michigan.
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Date Created: 10/08/16
Lecture 8: Introduction to Inference and Understanding Sampling Distributions 9.1 Parameters, Statistics, and Statistical Inference - Some distinctions to keep in mind: ▯ Population versus Sample ▯ Parameter versus Statistic - Population: Parameter, population proportion, population mean - Sample: Sample mean, sample proportion, statistic Statistical Inference: - the use of sample data to make judgments or decisions about populations. Confidence Interval Estimation: - A confidence interval is a range of values that the researcher is fairly confident will cover the true, unknown value of the population parameter. In other words, we use a confidence interval to estimate the value of a population parameter. Hypothesis Testing: - Hypothesis testing uses sample data to attempt to reject a hypothesis about the population. 9.2 From Curiosity to Questions About Parameters - The Big 5 are the commonly used five parameters 9.3 Overview of Sampling Distributions Sampling distribution of a statistic: - The distribution of all possible values of a statistic for repeated samples of the same size from a population is called the sampling distribution of the statistic. 9.4 Normal Approximation to the Binomial Distribution If X is a binomial random variable based on n trials with success probability p, and n is large, then the random variable X is also approximately N(np, ????????(1 − ????)) Conditions: The approximation works well when both np and n(1 – p) are at least 10. - If n is small (either np or n(1-p) less than 10), - > use binomial distribution to work out question - If n is large, -> use normal approximation OR related normal approximation for sample proportion. Sampling Distribution of ????: If sample size n is large enough (namely ▯(▯▯▯) np>=10 and n(1-p) >=10), then ???? is approximately N(p, ) ▯ Standard Deviation of ????: sd(????) = ▯(▯▯▯) ) ▯ Standard deviation: approximately the average distance of the possible ???? values for repeated samples of the same size n, from the true population proportion p. Standard Error of ????: se(????) = ????(1 − ????) ???? Standard error: estimate of the standard deviation of ????.
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