The 99%

Calculate 50 confidence intervals at the 99% confidence level. You do not need to obtain new samples, simply calculate new intervals based on the sample means and standard deviations you have already collected. Using the plot_ci() function, plot all intervals and calculate the proportion of intervals that include the true population mean.

If you don't remember, here is the formula for the lower and upper bound for a 99% confidence level respectively:

$$ \overline{x} - 2.58 \times \frac{\sigma}{\sqrt(n)} $$

$$ \overline{x} + 2.58 \times \frac{\sigma}{\sqrt(n)} $$

This exercise is part of the course

Data Analysis and Statistical Inference

View Course

Exercise instructions

Calculate lower and upper bounds using the formula described above.
Inspect the plot that was generated with the provided custom function plot_ci().

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

# Initialize samp_mean, samp_sd and n:
samp_mean <- rep(NA, 50)
samp_sd <- rep(NA, 50)
n <- 60

# For loop goes here:
for (i in 1:50) {
  samp <- sample(population, n) 
  samp_mean[i] <- mean(samp)
  samp_sd[i] <- sd(samp)
}

# Calculate the interval bounds here:
lower <-  
upper <- 

# Plotting the confidence intervals:
pop_mean <- mean(population)
plot_ci(lower, upper, pop_mean)

Edit and Run Code