Population table withcolumn serial number np arange 1

[ ]: population = Table() . with_column( "serial number" , np . arange( 1 , 150+1 ))
new_observations = population . sample(num_observations, with_replacement = True )
new_mean_based_estimate = mean_based_estimator(new_observations . column( 0 ))
new_bootstrap_estimates = sample_estimates(new_observations, ␣
, →
mean_based_estimator, 10000 )
Table() . with_column( "mean-based estimate" , new_bootstrap_estimates) .
, →
hist(bins = np . arange( 0 , 252 , 4 ))
new_left_end = percentile( 2.5 , new_bootstrap_estimates)
new_right_end = percentile( 97.5 , new_bootstrap_estimates)
[33]: population = Table() . with_column( "serial number" , np . arange( 1 , 150+1 ))
new_observations = population . sample(num_observations, with_replacement = True )
new_mean_based_estimate = mean_based_estimator(new_observations . column( 0 ))
new_bootstrap_estimates = sample_estimates(new_observations, ␣
, →
mean_based_estimator, 10000 )
Table() . with_column( "mean-based estimate" , new_bootstrap_estimates) .
, →
hist(bins = np . arange( 0 , 252 , 4 ))
12

new_left_end = percentile( 2.5 , new_bootstrap_estimates)
new_right_end = percentile( 97.5 ,new_bootstrap_estimates)
# Don't change code below this line!
print ( "New mean-based estimate: {:f} " . format(new_mean_based_estimate))
print ( "Middle 95 % o f bootstrap estimates: [ {:f} , {:f} ]" . format(new_left_end, ␣
, →
new_right_end))
plt . plot(make_array(new_left_end, new_right_end), make_array( 0 , 0 ), ␣
, →
color = 'yellow' , lw =3 , zorder =1 )
plt . scatter( 150 , 0 , color = 'red' , s =30 , zorder =2 );
New mean-based estimate: 152.705882
Middle 95% of bootstrap estimates: [112.352941, 193.058824]
[34]: ok . grade( "q3_2" );
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 2
Failed: 0
13

[ooooooooook] 100.0% passed
Question 3.3 Does the interval covering the middle 95% of the new bootstrap estimates include
N ? If you ran that cell 100 times and generated 100 intervals, how many of those intervals would
you expect to include N ?
Let’s look at what happens when we use a small number of resamples:
Question 3.4 In the cell below, explain why this histogram and confidence interval look different
from the ones you generated previously in Question 3.2 where the number of resamples was 10,000.
1.4 4. The CLT and Book Reviews
Your friend has recommended you a book, so you look for it on an online marketplace. You decide
to look at reviews for the book just to be sure that it’s worth buying. Let’s say that on Amazon,
the book only has 80% positive reviews. On GoodReads, it has 95% positive reviews. You decide
to investigate a bit further by looking at the percentage of positive reviews for the book on 5
different websites that you know of, and you collect these positive review percentages in a table
called reviews.csv .