handout_5_1_fall11(1) - 5.1 The Sampling Distribution of a...

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Unformatted text preview: 5.1 The Sampling Distribution of a Sample Mean (old 5.2) averages are less variable than individual observations averages are more normal than individual observations The mean and standard deviation of x x = mean of sample, = mean of population, 2 = population variance select an SRS of size n from a population and measure variable X on each individual in sample the n measurements are values of n random variables- X 1 , X 2 X n X i is measurement on one individual selected at random from population then X i has the distribution of the population if population is large relative to the size of the sample X 1 , X 2 X n considered independent Mean and standard deviation of a sample mean Let x be the mean of an SRS of size n from a population having mean and standard deviation . The mean and standard deviation of x are: x = x = n increasing sample size reduces sampling variability Sampling distribution of a sample mean If a population has the N(, ) distribution, then the sample mean x of n independent observations has the N(, n ) distribution....
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handout_5_1_fall11(1) - 5.1 The Sampling Distribution of a...

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