In David Eagleman’s book “Incognito”, the author mentions an experiment in which a human gene for color vision was spliced into the DNA of color-blind rats to try to give them color vision. The experiment involved two buttons, one red and one blue (with randomized locations), and the rats got a reward for pushing the blue button. Rats underwent a “learning phase” in which they were conditioned to associate the blue button with a reward, and after this phase, researchers could measure what percentage of attempts rats with the color-vision gene hit the blue button. To show the effectiveness of the added DNA, researchers needed the rats to get the reward more often than chance. How many attempts should the researchers plan to use (after the learning phase) if they want a power of (at least) 0.85 assuming the true blue-button percentage after training is 63%? Use α = 0.02, define a variable, state hypotheses, and include a picture with your solution that has two distributions drawn. (Use R, not tables.)
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