From the Introduction to Modern Statistics (IMS) textbook, complete the following exercises:

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Additionally, complete the following exercise using R:

Question #1: For this question you’ll use the data provided below, which are a random sample of \(n=200\) ICU patients from a research hospital affiliated with Carnegie Mellon University (CMU).

https://remiller1450.github.io/data/ICUAdmissions.csv

These data contain several categorical variables that are encoded numerically. The questions below will involve the variables:

Part A: According US Census data, the population of the Pittsburgh, PA metropolitan area (where CMU is located) is 85% white, 8% black, and 7% other races. Based upon this information, do any racial groups appear to be disproportionately represented among the ICU patients at this hospital? Your answer should: clearly state a null hypothesis, provide a table of expected counts, provide the test statistic, provide the p-value, and make a conclusion. You are welcome to use R functions to obtain any or all of these required items.

Part B: Using a Chi-Squared test, do these data provide statistical evidence of a difference in survival depending upon the level of consciousness of a patient arriving at the ICU? Your answer should: Your answer should: clearly state a null hypothesis, provide a table of expected counts, provide the test statistic, provide the p-value, and make a conclusion. You are welcome to use R functions to obtain any or all of these required items.

Part C: Consider the hypothesis test you performed in Part B. Based upon the table of expected counts do you believe this test to be a statistically reliable choice? That is, would a statistician have an issue with using this particular hypothesis test given the assumptions it requires?

Part D: Repeat the hypothesis test in Part B using Fisher’s exact test. How does the \(p\)-value differ from the one you found in Part B?

Part E: Use these data to evaluate whether it is statistically plausible that all three recorded levels of consciousness are equally likely among new arrivals to the ICU. Your answer should: clearly state a null hypothesis, provide a table of expected counts, provide the test statistic, provide the p-value, and make a conclusion. You are welcome to use R functions to obtain any or all of these required items.