Exercise 13. Estimating the probability of a specific error size
Assume you are in a practical situation and you don't know \(p\). Take a sample of size \(N=100\) and obtain a sample average of \(\bar{X} = 0.51\).
What is the CLT approximation for the probability that your error size is equal or larger than 0.01?
This exercise is part of the course
HarvardX Data Science Module 4 - Inference and Modeling
Exercise instructions
- Calculate the standard error of the sample average using the
sqrtfunction. - Use
pnormtwice to define the probabilities that a value will be less than -0.01 or greater than 0.01. - Combine these results to calculate the probability that the error size will be 0.01 or larger.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Define `N` as the number of people polled
N <-100
# Define `X_hat` as the sample average
X_hat <- 0.51
# Define `se_hat` as the standard error of the sample average
# Calculate the probability that the error is 0.01 or larger