Statistics324_HW4 - Statistics 324 Discussion 311 w/ Jack...

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Statistics 324 – Discussion 311 w/ Jack Homework 4 – Victoria Yakovleva 1. mn <- replicate(50000, mean(rnorm(4, mean = 100, sd = 20))) mean(mn) [1] 99.99353 This is close to µ=100. var(mn) [1] 100.7322 The theoretical variance of the sample mean of samples of size 4 from a normal distribution with mean, µ=100, and standard deviation, s=20: (20^2)/4 = 100 sd(mn) [1] 10.03654 The theoretical standard deviation of the distribution of the sample means: 100^(1/2) = 10 The sample variance and sample standard deviation are close to the theoretical values. EMPIRICAL DENSITY PLOT: NORMAL PROBABILITY PLOT:
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2. mn2 <- replicate(50000, mean(rnorm(16, mean = 100, sd = 20))) mean(mn2) [1] 100.0038 This is close to µ=100. var(mn2) [1] 24.98805 The theoretical variance of the sample mean of samples of size 16 from a normal distribution with mean, µ=100, and standard deviation, s=20: (20^2)/16 = 25 sd(mn2) [1] 4.998805 The theoretical standard deviation of the distribution of the sample means: 25^(1/2) = 5 The sample variance and sample standard deviation are close to the theoretical values. EMPIRICAL DENSITY PLOT: NORMAL PROBABILITY PLOT:
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3. mn3 <- replicate(50000, mean(rnorm(64, mean = 100, sd = 20))) mean(mn3) [1] 99.99354 This is close to µ=100. var(mn3)
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This note was uploaded on 03/27/2008 for the course STAT 324 taught by Professor Bates during the Fall '06 term at University of Wisconsin Colleges Online.

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Statistics324_HW4 - Statistics 324 Discussion 311 w/ Jack...

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