# Question 5 explain whether you believe you can

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Question 5. Explain whether you believe you can accurately use a sample size of 500 to determine the maximum. What is one problem with using the maximum as your estimator? Use the histogram above to help answer. BEGIN QUESTION name: q4_5 manual: true
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. We play the game once and we lose, observing 1 head. We are angry and accuse Gary of cheating! Gary is adamant, however, that the coin is fair. Gary’s model claims that there is an equal chance of getting heads or tails, but we do not believe him. We believe that the coin is clearly rigged, with heads being less likely than tails. 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. Since we’re working with probabilities, 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 expected number of heads in 10 flips (5) 13
2. The expected number of heads in 10 flips 3. The actual number of heads we get in 10 flips BEGIN QUESTION name: q5_2 manual: false [9]: statistic_choice = 3 #SOLUTION statistic_choice [9]: 3 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 Question 1), 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 . BEGIN QUESTION name: q5_3 manual: false [14]: def coin_simulation_and_statistic (sample_size, model_proportions): # BEGIN SOLUTION simulation = sample_proportions(sample_size, model_proportions) statistic = sample_size * simulation . item( 0 ) return statistic # END SOLUTION coin_simulation_and_statistic( 10 , coin_model_probabilities) [14]: 5.0