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NOTES_Chapter 9_Sampling Distributions

# NOTES_Chapter 9_Sampling Distributions - Chapter 9 Sampling...

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Chapter 9: Sampling Distributions 9.1 Sampling Distribution of the Mean Two methods to create a sampling distribution o Draw samples of the same size from a population, calculate the statistic of interest, and then use descriptive techniques to learn more about the sampling distribution o The second method relies on the rules of probability and the laws of expected value and variance to derive the sampling distribution Sampling Distribution of the Mean of Two Dice o Population Statistics Population mean Population Variance Population standard deviation Because the value of the sample mean varies randomly from sample to sample, we can regard as a new random variable created by sampling o Sampling Statistics The most interesting aspect of the sampling distribution of is how different it is from the distribution of Mean of the sampling distribution of Variance of the sampling distribution of Standard deviation of the sampling distribution of It is important to recognize that the distribution of is different from the distribution of However, the two random variables are related; their means are the same and their variances are related The variance of the sampling distribution of is less than the variance of the population we’re sampling from all sample sizes Thus, a randomly selected value of is likely to be closer to the mean value than is a randomly selected value of As gets larger, the sampling distribution of becomes increasingly bell shaped o Central Limit Theorem The sampling distribution of the mean of a random sample drawn from any population is approximately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution of will resemble a normal distribution.

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