Stats Final Exam Notes

Stats Final Exam Notes - Stats Final Exam Notes Ch 8 9 10...

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Stats Final Exam Notes: Ch. 8, 9, 10, 12, & 14 Chapter 8: Sampling Distributions and Estimation Sampling Variation o sampling variation : sample statistics will vary from sample to sample o some samples may represent the population well, while other samples could differ greatly from the population (particularly if the sample size is small) o population parameters remain fixed as long as the population remains the same o process parameters remain fixed as long as the process remains the same o sometimes we know a parameter value and sometimes we don’t o the value of a statistic can change whenever we take a new sample Sampling Distribution o sampling distribution : the probability distribution of all possible values the statistic may assume when a random sample of size n is taken o when we use a sample statistic to make conclusions about a population parameter, we are interested in __________ o sampling distribution is the pattern we would see if we looked at all possible statistic values from all samples of the same size we look for the shape, center, and spread o population size does not influence sampling variability What does? …….Sample size! rule of thumb: provided the population is 100 times larger than the sample good random sample o x is a random variable varies from sample to sample o Distribution of x
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suppose X is a random variable. If x is the mean of a simple random sample of size n , then the distribution of x can be described with the above parameters Law of Large Numbers o the larger the sample drawn the closer the sample mean gets to the population mean x µ as n gets closer to N Central Limit Theorem o central limit theorem : a powerful result that allows us to approximate the shape of the sample distribution of x even when we don’t know the shape of the population distribution o if the population distribution is not normal . we can determine the probability that a sample mean falls in an interval no matter what the sample size because the sampling distribution will be approximately normal when we take numerous samples of size 30 or more o if the population distribution is norma l, we can determine the probability that a
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