DATA ANALYSIS > QUESTIONS & ANSWERS > University of California, Berkeley DATA MISC ProfMask8468 (All)

University of California, Berkeley DATA MISC ProfMask8468

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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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