Confidence intervals
Now let's return for a moment to the question that first motivated this lab: based on this sample, what can we infer about the population?
Based only on this single sample, the best estimate of the average living area of houses sold in Ames would be the sample mean, usually denoted as \(\overline{x}\) (here we're calling it sample_mean).
That serves as a good point estimate but it would be useful to also communicate how uncertain we are of that estimate. This can be captured by using a confidence interval.
We can calculate a 95% confidence interval for a sample mean by adding and subtracting 1.96 standard errors to the point estimate.
se <- sd(samp)/sqrt(60)
lower <- sample_mean - 1.96 * se
upper <- sample_mean + 1.96 * se
c(lower, upper)
It is an important inference that we make with this: even though we don't know what the full population looks like, we're 95% confident that the true average size of houses in Ames lies between the values lower and upper.
This exercise is part of the course
Data Analysis and Statistical Inference
Exercise instructions
Calculate the 95% confidence interval as described above.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# The ames data frame is already loaded into the workspace,
# as are population, samp and sample_mean
# Calculate the standard error:
se <-
# Calculate the lower and upper bounds of your confidence interval and print them:
lower <-
upper <-