{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Statistics324_HW4

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

This preview shows pages 1–4. Sign up to view the full content.

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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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:
3. mn3 <- replicate(50000, mean(rnorm(64, mean = 100, sd = 20))) mean(mn3) [1] 99.99354 This is close to µ=100. var(mn3) [1] 6.271652 The theoretical variance of the sample mean of samples of size 64 from a normal distribution with mean, µ=100, and standard deviation, s=20: (20^2)/64 = 6.25

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}