Before connecting the encoder and decoder rats, the researchers wanted to verify that the decode rats were sufficiently trained to choose the correct lever when seeing a visual cue. After training, one of the decoder rats was tested 25 times on his ability to select the "correct" lever. He selected the correct lever 19 times.
(a) Compute a 95% Wilson-adjusted confidence interval for the accuracy rate for this rat and interpret the interval in the context of the question.
(b) Using your interval computed in part (a) to support your answer, are you convinced that this rat's accuracy rate is better than simple guessing (i.e., 50% accuracy)?
(c) Using your interval computed in part (a) to support your answer, are you convinced that this rat's accuracy rate is better than 70%?
(d) Use a χ2 goodness-of-fit test, to test whether or not the accuracy rate exceeds 70%. Use α = 0.05.