(20 points) Chronic traumatic encephalopathy (CTE) is a neurodegenerative disease linked to repeated blows to the head.

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20 Points Chronic Traumatic Encephalopathy Cte Is A Neurodegenerative Disease Linked To Repeated Blows To The Head 1 (82.34 KiB) Viewed 106 times

(20 points) Chronic traumatic encephalopathy (CTE) is a neurodegenerative disease linked to repeated blows to the head. Professional athletes in combat sports, such as boxing and mixed martial arts, or contact sports, such as American football or ice hockey, are known to be at greater risk. Currently CTE can only be definitively diagnosed through post-mortem autopsy. So it is not possible to test professional athletes and accurately determine the prevalence of CTE. Available data is based entirely on the prevalence of CTE among deceased athletes whose brains were donated for research. Suppose you are a researcher trying to understand the risk of CTE for professional athletes. Come up with confidence intervals based on the limited number of sample you have. (a) (4 pts) Suppose that, out of the 100 deceased athletes whose brains have been donated, 40% of them are diagnosed with CTE. Find a two-sided 95% confidence interval. (b) (4 pts) Suppose that, out of the 900 deceased athletes whose brains have been donated, 40% of them are diagnosed with CTE. Find a two-sided 95% confidence interval. (c) (4 pts) Compare the intervals you got in (a) and (b). Which one is a larger interval. Conceptually explain why that is the case. (d) (4 pts) Suppose that, out of the 900 deceased athletes whose brains have been donated, 450 of them are diagnosed to have had CTE. Find a two-sided 99% confidence interval. (e) (4 pts) Compare the intervals you got in (b) and (d). Which one is a larger interval. Conceptually explain why that is the case.