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Create variables called sam20means and sam50means that contains the means of the samples. Use a density...

Create variables called sam20means and sam50means that contains the means of the samples. Use a density plot to show the sampling distribution of the means for sam20means and sam50means together.

????Compare the Standard Error (SE) of the sampling distributivos. Which sample size creates better estimates of the population mean (ie. has the lowest SE). Solve using R.????

Expert Solution

Create variables called sam20means and sam50means that contains the means of the samples. Use a density plot to show the sampling distribution of the means for sam20means and sam50means together.

Let us create samples from normal distribution with mean 20 and with sd 2.

R code:

sam20<-rnorm(20, 20,2)

sam50<-rnorm(50, 20,2)

d1 <- density(sam20)

d2 <- density(sam50)

par(mfrow=c(1,2))

plot(d1)

plot(d2)

se20<-sd(sam20)/sqrt(20);se20

se50<-sd(sam50)/sqrt(50);se50

R output:

se20<-sd(sam20)/sqrt(20);se20

[1] 0.3716666

> se50<-sd(sam50)/sqrt(50);se50

[1] 0.2653752

??Compare the Standard Error (SE) of the sampling distributivos. Which sample size creates better estimates of the population mean (ie. has the lowest SE). Solve using R.

Standard Error (SE) of the sampling distribution with n=20 is 0.3717

Standard Error (SE) of the sampling distribution with n=50 is 0.2654

The sample with size 50 creates better estimates of the population mean (ie. has the lowest SE).

milcah answered 6 months ago

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