</div> #### Question 2
She then wants to use 10,000 bootstrap resamples to compute a confidence interval for the
proportion of all California voters who will vote Yes. Fill in the next cell to simulate an empiri-
cal distribution of Yes proportions with 10,000 resamples. In other words, use bootstrap resam-
pling to simulate 10,000 election outcomes, and populate
resample_yes_proportions
with the
yes proportion of each bootstrap resample. Then, visualize
resample_yes_proportions
with a
histogram. You should see a bell shaped curve centered near the proportion of Yes in the original
sample.

18

In [27]:
_
=
ok
.
grade(
'
q3_2
'
)
_
=
ok
.
backup()
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
<IPython.core.display.Javascript object>
<IPython.core.display.Javascript object>
Saving notebook... Saved
'
hw09.ipynb
'
.
Backup... 100% complete
Backup successful for user: [email protected]
URL:
NOTE: this is only a backup. To submit your assignment, use:
python3 ok --submit
19

</div> #### Question 3 Why does the Central Limit Theorem (CLT) apply in this situation,
and how does it explain the distribution we see above?

20

</div> In a population whose members are 0 and 1, there is a simple formula for the standard
deviation of that population:
standard deviation
=
√
(
proportion of 0s
)
×
(
proportion of 1s
)
(Figuring out this formula, starting from the definition of the standard deviation, is an fun
exercise for those who enjoy algebra.)
21

</div> #### Question 4 Using only the CLT and the numbers of Yes and No voters in our
sample of 400, compute (
algebraically
) a number
approximate_sd
that’s the predicted standard
deviation of the array
resample_yes_proportions
according to the Central Limit Theorem.
Do
not access the data in
resample_yes_proportions
in any way.
Remember that a predicted stan-
dard deviation of the sample means can be computed from the population SD and the size of the
sample.
Also remember that if we do not know the population SD, we can use the sample SD as a
reasonable approximation in its place.
In [28]:
approximate_sd
=
((
210/400
)
*
(
190/400
)
/ 400
)
** 0.5
approximate_sd
Out[28]:
0.02496873044429772
In [29]:
_
=
ok
.
grade(
'
q3_4
'
)
_
=
ok
.
backup()
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
<IPython.core.display.Javascript object>
<IPython.core.display.Javascript object>
Saving notebook... Saved
'
hw09.ipynb
'
.