1. A paper by Murphy et al. (2020) describes the result of a study where an artificial intelligence (AI) machine was taught to read

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1. A paper by Murphy et al. (2020) describes the result of a study where an "artificial intelligence" (AI) machine was taught to read chest X-rays and determine whether or not the result was specifically a pneumonia consistent with Covid. X-rays of 454 people with and without Covid were shown to both the AI and professional radiologists. Each examiner gave their judgment as to whether the image was positive or negative for Covid pneumonia. Table 2 shows an alterd version of the data set for comparing the test accuracies for the sample of Xrays from non-Covid patients. Here, for both Human and AI readers, "success" (=1) is when the reader correctly identifies no Covid. (a) Estimate the probability that the two tests agree on the outcome. (b) Estimate the probability that the human reader gives a correct diagnosis. Repeat for the AI. (c) Explain what +1 1+ measures in the context of this problem. (d) Calculate the score confidence interval for +1 1+ (e) Perform a hypothesis test of Ho+11+ = 0 vs. H: +1 T1+ 0 using McNemar's test. Report the test statistic and p-value. (f) Interpret the intervals and the hypothesis test results in the context of the data, and draw conclusions about whether one reader seems to have a different probability of returning a positive result than the other. (In other words, what did the researchers' data tell them, and what evidence are you using to form that conclusion?) Table 2: Data comparing AI and Human readings of the same X-rays. All patients were non-Covid. For each reading, 1 means the reader got it right and 0 means they got it wrong. 0 1 Total 0 94 128 222 Human 1 101 131 232 Total 195 259 454