lab06-Revised-Bailey-Jun10-2022

Question 2: Remember that the practitioner got the correct answer 44% (0.44) of the time. According to the null model, on average, what proportion of times do we expect the practitioner to guess the correct hand? Make sure your answer is between 0 and 1. [3]: expected_proportion_correct = 0.5 model_proportions = make_array(expected_proportion_correct, 1 - ␣ , → expected_proportion_correct) model_proportions [3]: array([0.5, 0.5]) [4]: #grader.check("q1_2") Question 3: In the code cell below we will provide a simulation that will test whether the TT practitioners results are consistent with their claims that they can sense an HEF. Just run the cell below. [5]: actual_proportion = 0.44 def statistic (expected_prop_correct, actual_prop): return 100* (actual_prop - expected_prop_correct) observed_statistic = statistic(expected_proportion_correct, actual_proportion) def simulation_and_statistic (model_proportions, expected_prop_correct): '''Simulates 210 TT hand choices under the null model. Returns one statistic from the simulation.''' simulation_proportion_correct = sample_proportions( 210 , model_proportions) . , → item( 0 ) one_statistic = expected_prop_correct - 100* simulation_proportion_correct return one_statistic num_repetitions = 5000 simulated_statistics = make_array() for i in np . arange(num_repetitions): simulated_statistics = np . append(simulated_statistics, ␣ , → simulation_and_statistic(make_array( 0.5 , 0.5 ), 50 )) p_value = sum (simulated_statistics <= -6.0 ) / num_repetitions print ( f"A single trial was 210 selections, and this simulation consisted of ␣ , → { num_repetitions } trials. \n The p-value for this simulation is { p_value } ." ) A single trial was 210 selections, and this simulation consisted of 5000 trials. The p-value for this simulation is 0.0402. 3

Remember, since this researcher is working to disprove Emily, the alternative hypothesis would be different. H o : π = 0 . 5 H a : π > 0 . 5 [10]: # Run the binom_test in this cell stats . binom_test( 115 , 210 , 0.5 , alternative = "greater" ) [10]: 0.09484499448959463 Because the P-value is less than 0.5 we accept the alternatice Question 8: At the 5% level of significance, what is the least number of successes this second researcher must find in a sample of 210 trials in order for the binom_test to yield a p-value small enough to reject the null hypothesis? [55]: # Let least_successes represent the answer to the question above. least_successes = 105 [56]: # If you've answered the above question right, this test should have a p-value ␣ , → below 0.05 stats . binom_test(least_successes, 210 , 0.5 , alternative = "greater" ) [56]: 0.5274968790385095 Congratulations! You’re done with Lab 6. Download this file in the format(s) your instructor requires and submit to the Lab 6 folder under Assignments. [ ]: 6