The sampling distribution
Not surprisingly, every time we take another random sample, we get a different sample mean. It's useful to get a sense of just how much variability we should expect when estimating the population mean this way.
The distribution of sample means, called the sampling distribution, can help us understand this variability. In this lab, because we have access to the population, we can build up the sampling distribution for the sample mean by repeating the above steps many times. Here we will generate 5000 samples and compute the sample mean of each.
The code in the editor takes 5000 samples of size 50 from the population, calculates the mean of each sample, and stores each result in a vector called sample_means50, using what we call a for loop.
If this is completely new to you, do not fear, in the next exercises we'll review in detail how these lines of code work.
This exercise is part of the course
Data Analysis and Statistical Inference
Exercise instructions
- Inspect the code in the editor.
- Run it to see what it does, try and see if you can more or less understand how it works.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# The ames data frame and area and price objects are already loaded into the workspace
# Set up an empty vector of 5000 NAs to store sample means:
sample_means50 <- rep(NA, 5000)
# Take 5000 samples of size 50 of area and store all of them in sample_means50.
for (i in 1:5000) {
samp <- sample(area, 50)
sample_means50[i] <- mean(samp)
}
# View the result. If you want, you can increase the bin width to show more detail by changing the breaks argument.
hist(sample_means50, breaks = 13)