large enough to achieve that. (Polling is expensive, so the sample also shouldn’t be bigger than
necessary.)
Michelle consults Chapter 14 of your textbook. Instead of making the conservative assumption
that the population standard deviation is 0.5 (coding Yes voters as 1 and No voters as 0), she
decides to assume that it’s equal to the standard deviation of the sample,
√
(
Yes proportion in the sample
)
×
(
No proportion in the sample
)
.
Under that assumption, Michelle decides that a sample of 9,975 would suffice.
Question 7
Does Michelle’s sample size achieve the desired standard deviation of sample
means?
What SD would you achieve with a smaller sample size?
A higher sample size?
To
explore this, first compute the SD of sample means obtained by using Michelle’s sample size.

Question 8
Then, compute the SD of sample means that you would get from a smaller sample size. Ideally,
you should pick a number that is significantly smaller, but any sample size smaller than Michelle’s
will do.

23

With this smaller sample size, you would predict a sample mean SD of 0.015792
In [48]:
ok
.
grade(
"q3_8"
);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
Question 9
Finally, compute the SD of sample means that you would get from a larger sample size. Here,
a number that is significantly larger would make any difference more obvious, but any sample
size larger than Michelle’s will do.
In [51]:
larger_sample_size
= 20000
larger_sample_mean_sd
=
estimated_population_sd
/
(larger_sample_size
**0.5
)
print
(
"With this larger sample size, you would predict a sample mean SD of
%f
"
%
large
With this larger sample size, you would predict a sample mean SD of 0.003531
In [52]:
ok
.
grade(
"q3_9"
);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
Question 10
Based off of this, was Michelle’s sample size approximately the minimum suffi-
cient sample, given her assumption that the sample SD is the same as the population SD? Assign
min_sufficient
to
True
if this 9975 was indeed approximately the minimum sufficient sample,
and
False
if it wasn’t.
In [53]:
min_sufficient
=
True
min_sufficient
24

Out[53]:
True
In [54]:
ok
.
grade(
"q3_10"
);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
1.4
4. Submission
Once you’re finished, select "Save and Checkpoint" in the File menu and then execute the
submit
cell below. The result will contain a link that you can use to check that your assignment has been
submitted successfully. If you submit more than once before the deadline, we will only grade your
final submission. If you mistakenly submit the wrong one, you can head to
okpy.org