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GG274 Homework 9: Bootstrap Confidence Intervals

GG274 Homework 9: Bootstrap Confidence Intervals#

Logistics#

Due date: The homework is due 23:59 on Monday, March 18.

You will submit your work on MarkUs. To submit your work:

  1. Download this file (Homework_9.ipynb) from JupyterHub. (See our JupyterHub Guide for detailed instructions.)

  2. Submit this file to MarkUs under the hw9 assignment. (See our MarkUs Guide for detailed instructions.) All homeworks will take place in a Jupyter notebook (like this one). When you are done, you will download this notebook and submit it to MarkUs.

Introduction#

In this homework you will construct a bootstrap confidence interval around a sample mean of time spent driving, for those people in the survey who reported more than 0 minutes of driving.

import pandas as pd
import matplotlib.pyplot as plt 
import numpy as np
import seaborn as sns

durl313            Duration - Travel - Car - Driver

           VALUE  LABEL
               0  No time spent doing this activity
            9996  Valid skip
            9997  Don't know
            9998  Refusal
            9999  Not stated

           Data type: numeric
           Missing-data codes: 9996-9999
           Record/columns: 1/362-364

Step 1 - Read the time use survey data into a pandas DataFrame#

a) The data is stored in gss_tu2016_main_file.csv .

Use the pandas function read_csv to read the data into a pandas DataFrame named time_use_df.

# Write your code below
time_use_df = pd.read_csv('gss_tu2016_main_file.csv')

b) Use time_use_df to create a another DataFrame called drive_time_df that has two columns: 'CASEID', 'durl313' (in that order).

# Write your code below
drive_time_df = time_use_df[["CASEID", "durl313"]]

drive_time_df.head()
CASEID durl313
0 10000 90
1 10001 0
2 10002 30
3 10003 80
4 10004 0

b) Rename the column names of drive_time_df using the following table. The DataFrame with the new column names should be called drive_time_df (i.e., don’t change the name of the DataFrame).

Original column name

New column name

CASEID

ID

durl313

drv_time

 
# Write your code below
column_names = {'CASEID': 'ID',
                'durl313': 'drv_time'}

drive_time_df = drive_time_df.rename(columns=column_names)

Step 2 - Select only those participants who drove and create new pandas DataFrame.#

a) In this step you will select only those survey participants who drove (i.e., their drv_time value is greater than 0 and not 9996, 9997, 9998, or 9999.

First, create a pandas Series called driver where a value is True if the person drove and False if they did not.

# Write your code below

driver = (drive_time_df["drv_time"] > 0) & (drive_time_df["drv_time"] < 9996)

b) Create a new DataFrame subset_drive_time_df by selecting the rows in drive_time_df where the person drove.

# Write your code below
subset_drive_time_df = drive_time_df[driver]

Step 3 - Calculate the mean of how much time drivers spent driving#

In this step you will compute the mean of how much time drivers spent driving and store it in a variable called drive_time_avg.

# Write your code below

drive_time_avg = subset_drive_time_df['drv_time'].mean()

Step 4 - Create a function that generates a bootstrap sample from subset_drive_time_df#

In the below cell, create a function called one_bs_mean that calculates a bootstrap sample mean called dt_bsmean_sample from subset_drive_time_df.

# Write your code below

def one_bs_mean():
    dt_bsmean_sample = subset_drive_time_df['drv_time'].sample(frac = 1, replace=True).mean()
    return dt_bsmean_sample

# test your function
one_bs_mean()

74.5740412979351

Step 5 - Compute a distribution of bootstrap sample means#

a) Create an empty list called bootstrap_means and then a loop that populates this list with 10,000 bootstrap sample means (generated from calling your one_bs_mean function).

# This code sets a random seed so the code below generates the same results
# Don't change this!
np.random.seed(901)

# Write your code below
bootstrap_means = []
for _ in range(10000):
    bootstrap_means.append(one_bs_mean())

b) Plot bootstrap_means as a histogram using a color argument of cyan and edgecolor of red. Save the histogram to bootstrap_means_histogram.

# Write your code below
bootstrap_means_histogram = plt.hist(bootstrap_means, color = 'cyan', edgecolor = 'red')
../../../../_images/857e1c8e26b3107b8e39b290043c2a9824ec116f551ffaaa34e2346b66f06589.png

Step 6 - Report the 95% confidence interval of the sample mean of how much time drivers spend driving#

a) Compute the 2.5th percentile from the distribution bootstrap_means using the np.percentile(). Save the percentile to bootstrap_means_2p5_percentile.

# Write your code below
bootstrap_means_2p5_percentile = np.percentile(bootstrap_means, 2.5)

bootstrap_means_2p5_percentile

73.98493117010815

b) Compute the 97.5th percentile from the distribution bootstrap_means using the np.percentile(). Save the percentile to bootstrap_means_97p5_percentile.

# Write your code below
bootstrap_means_97p5_percentile = np.percentile(bootstrap_means, 97.5)

bootstrap_means_97p5_percentile

76.78839724680432

c) Complete the following sentence reporting the 95% bootstrap confidence interval, rounded to two decimal points.

write answer here

ANSWER: A 95% bootstrap confidence interval for the sample mean of driving time for drivers is 73.98 to 76.79 minutes.

Give this to students: “A 95% bootstrap confidence interval for the sample mean of driving time for drivers is __ to __ minutes.

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