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5_2_Handout

# 5_2_Handout - 5.2 The Sampling Distribution of a Sample...

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5.2 The Sampling Distribution of a Sample Mean Figure 5.8 •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 μ = mean of population σ 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 μ and standard deviation σ. The mean and standard deviation of x are: μ x = μ σ x = σ/ n

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EX - length of service calls x = σ/ n ) σ = 184.81 seconds SRS of 20 calls: σ x = SRS of 80 calls: σ x = •averaging over more calls reduces variability- makes it more likely that
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5_2_Handout - 5.2 The Sampling Distribution of a Sample...

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