lab07October 17, 20180.1 Lab 7: Resampling and the BootstrapThe British Royal Air Force wanted to know how many warplanes the Germans had (some number N, which is a population parameter), and they needed to estimate that quantity knowing only arandom sample of the planes’ serial numbers (from 1 to N). We know that the German’s warplanesare labeled consecutively from 1 to N, so N would be the t
October 17, 2018
0.1 Lab 7: Resampling and the Bootstrap
The British Royal Air Force wanted to know how many warplanes the Germans had (some number N, which is a population parameter), and they needed to estimate that quantity knowing only a
random sample of the planes’ serial numbers (from 1 to N). We know that the German’s warplanes
are labeled consecutively from 1 to N, so N would be the total number of warplanes they have.
We normally investigate the random variation amongst our estimates by simulating a sampling procedure from the population many times and computing estimates from each sample that
we generate. In real life, if the RAF had known what the population looked like, they would have
known N and would not have had any reason to think about random sampling. However, they
didn’t know what the population looked like, so they couldn’t have run the simulations that we
Simulating a sampling procedure many times was a useful exercise in understanding random
variation for an estimate, but it’s not as useful as a tool for practical data analysis.
Let’s flip that sampling idea on its head to make it practical. Given just a random sample
of serial numbers, we’ll estimate N, and then we’ll use simulation to find out how accurate our
estimate probably is, without ever looking at the whole population. This is an example of statistical
As usual, run the cell below to prepare the lab and the automatic tests.
In : # Run this cell to set up the notebook, but please don't change it.
# These lines import the Numpy and Datascience modules.
import numpy as np
from datascience import *
# These lines do some fancy plotting magic.
import matplotlib.pyplot as plt
# These lines load the tests.
from client.api.notebook import Notebook
ok = Notebook('lab07.ok')
_ = ok.auth(inline=True)