###############################################
Spread of a distribution with number of samples
###############################################

.. code-links:: clear

Have a look back at :doc:`brexit_proportions_solution`.  We found that our
sampling distribution of 1315 simulated voters with p=0.519 of voting Brexit
was not compatible with the survey proportion of 0.41.

We're going to be doing some plots, so we start of by getting the plotting
libraries:

.. mpl-interactive::

.. nbplot::

    >>> #: The stuff you need for plotting a histogram
    >>> import matplotlib.pyplot as plt

Let's have a look again at the sampling distribution:

.. nbplot::

    >>> #: The random module
    >>> import random

.. nbplot::
    :hide-from: all
    :show-to: doctest

    >>> random.seed(1966)

.. nbplot::

    >>> #: function to return a Leave or Remain voter
    >>> def leave_or_remain():
    ...     # Return 1 for Leave, 0 for Remain
    ...     random_no = random.random()
    ...     if random_no < 0.519:
    ...         our_result = 1
    ...     else:
    ...         our_result = 0
    ...     return our_result

Here we get 1315 voters, and calculate a *statistic*, the proportion of Brexit
voters:

.. nbplot::

    >>> #: The statistic value from a single trial
    >>> def one_proportion():
    ...     votes = []
    ...     for i in range(1315):
    ...         vote = leave_or_remain()
    ...         votes.append(vote)
    ...     brexits = sum(votes)
    ...     return brexits / len(votes)

Now we want the sampling distribution of this proportion:

.. nbplot::

    >>> n_trials = 10000
    >>> proportions = []
    >>> for i in range(n_trials):
    ...     proportion = one_proportion()
    ...     proportions.append(proportion)

Plot the histogram of the sampling distribution you have just collected:

.. nbplot::

    >>> #- plot the histogram of the sampling distribution
    >>> plt.hist(proportions)
    (...)

Now - go back to ``one_proportion`` above, and change 1315 to 20.  Plot the
sampling distribution again, by running the cells above.  What do you see?
Try 50, 100 and 1000 instead of 20.