Question 5.
Explain whether you believe you can accurately use a sample size of 500 to de-
termine the maximum. What is a specific con of using the maximum as your estimator? Use the
histogram above to help answer.

1.5
5. Assessing Gary’s Models
Games with Gary
Our friend Gary comes over and asks us to play a game with him. The game
works like this:
We will flip a fair coin 10 times, and if the number of heads is greater than or equal to
5, we win!
Otherwise, Gary wins.
13

Question 1
Assign
coin_model_probabilities
to a two-item array containing the chance of
heads as the first element and the chance of tails as the second element under Gary’s model. Make
sure your values are between 0 and 1.

Question 2
We believe Gary’s model is incorrect. In particular, we believe there to be a smaller chance
of heads. Which of the following statistics can we use during our simulation to test between the
model and our alternative? Assign
statistic_choice
to the correct answer.
1. The distance (absolute value) between the actual number of heads in 10 flips and the ex-
pected number of heads in 10 flips (5)
2. The expected number of heads in 10 flips
3. The actual number of heads we get in 10 flips

Question 3
Define the function
coin_simulation_and_statistic
, which, given a sample size
and an array of model proportions (like the one you created in Q1), returns the number of heads
in one simulation of flipping the coin under the model specified in
model_proportions
.
Hint:
Think about how you can use the function
sample_proportions
.

14

Out[103]:
0.5
In [104]:
_
=
ok
.
grade(
'
q5_3
'
)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
Question 4
Use your function from above to simulate the flipping of 10 coins 5000 times under the pro-
portions that you specified in problem 1. Keep track of all of your statistics in
coin_statistics
.