hw09
July 14, 2020
[1]: # Initialize OK
from client.api.notebook import Notebook
ok = Notebook('hw09.ok')
=====================================================================
Assignment: Resampling and the Bootstr
...
hw09
July 14, 2020
[1]: # Initialize OK
from client.api.notebook import Notebook
ok = Notebook('hw09.ok')
=====================================================================
Assignment: Resampling and the Bootstrap
OK, version v1.12.5
=====================================================================
1 Homework 9: Bootstrap, Resampling, CLT
Reading: * Estimation * Why the mean matters
Please complete this notebook by filling in the cells provided. Before you begin, execute the
following cell to load the provided tests. Each time you start your server, you will need to execute
this cell again to load the tests.
Homework 9 is due Thursday, 4/9 at 11:59pm. You will receive an early submission bonus point
if you turn in your final submission by Wednesday, 4/8 at 11:59pm. Start early so that you can
come to office hours if you’re stuck. Check the website for the office hours schedule. Late work will
not be accepted as per the policies of this course.
Directly sharing answers is not okay, but discussing problems with the course staff or with other
students is encouraged. Refer to the policies page to learn more about how to learn cooperatively.
For all problems that you must write our explanations and sentences for, you must provide your
answer in the designated space. Moreover, throughout this homework and all future ones, please be
sure to not re-assign variables throughout the notebook! For example, if you use max_temperature
in your answer to one question, do not reassign it later on.
As usual, run the cell below to import modules and autograder tests.
[2]: # 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 *
1
# These lines do some fancy plotting magic.
import matplotlib
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')
import warnings
warnings.simplefilter('ignore', FutureWarning)
# These lines load the tests.
from client.api.notebook import Notebook
ok = Notebook('hw09.ok')
_ = ok.submit()
=====================================================================
Assignment: Resampling and the Bootstrap
OK, version v1.12.5
=====================================================================
Saving notebook… Saved 'hw09.ipynb'.
Submit… 100% complete
Submission successful for user: [email protected]
URL: https://okpy.org/cal/data8/sp20/hw09/submissions/wKmnRz
1.1 1. Preliminaries
The British Royal Air Force wanted to know how many warplanes the Germans had (some number
N, which is a 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 among 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 British Royal Air Force (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 normally do.
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
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