More on sampling

Mechanics aside, let's return to the reason we used a for loop: to compute a sampling distribution, specifically, this one: hist(sample_means50). (Try it in the console!)

The sampling distribution that we computed tells us much about estimating the average living area in homes in Ames. Because the sample mean is an unbiased estimator, the sampling distribution is centered at the true average living area of the the population, and the spread of the distribution indicates how much variability is induced by sampling only 50 home sales.

Let's see what the effect is of the sample size on our distribution. Take a look at the code. In total we create three sampling stributions, sample_means10, sample_means50 (that we had coded before) and sample_means100.

This exercise is part of the course

Data Analysis and Statistical Inference

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Exercise instructions

Inspect the code and execute it.

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

# Initialize the sample distributions:
sample_means10 <- rep(NA, 5000)
sample_means50 <- rep(NA, 5000)
sample_means100 <- rep(NA, 5000)

# Run the for loop:
for (i in 1:5000) {
	samp <- sample(area, 10)
	sample_means10[i] <- mean(samp)
	samp <- sample(area, 50)
	sample_means50[i] <- mean(samp)
	samp <- sample(area, 100)
	sample_means100[i] <- mean(samp)
}

# Take a look at the results:
head(sample_means10)
head(sample_means50)
head(sample_means100)

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