Hepatic Disease Suppose we observe 84 alcoholics with cirrhosis of the liver, of whom 29 have hepatomas—that is, liver-cell carci-noma. Suppose we know, based on a large sample, that the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%. a- What is the probability that we observe exactly 29 alcoholics with cirrhosis of the liver who have hepatomas if the true rate of hepatoma among alcoholics (with or without cirrhosis of the liver) is .24? b-What is the probability of observing at least 29 hepa- tomas among the 84 alcoholics with cirrhosis of the liver under the assumptions in Problem a? c- What is the smallest number of hepatomas that would have to be observed among the alcoholics with cirrhosis of the liver for the hepatoma experience in this group to differ from the hepatoma experience among alcoholics without cirrhosis of the liver? (Hint: Use a 5% probability of getting a result at least as extreme to denote differences between the hepatoma experiences of the two groups.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Hepatic Disease
Suppose we observe 84 alcoholics with cirrhosis of the liver, of whom 29 have hepatomas—that is, liver-cell carci-noma. Suppose we know, based on a large sample, that the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%.
a- What is the probability that we observe exactly 29
alcoholics with cirrhosis of the liver who have hepatomas if
the true rate of hepatoma among alcoholics (with or without
cirrhosis of the liver) is .24?
b-What is the probability of observing at least 29 hepa-
tomas among the 84 alcoholics with cirrhosis of the liver
under the assumptions in Problem a?
c- What is the smallest number of hepatomas that would
have to be observed among the alcoholics with cirrhosis of
the liver for the hepatoma experience in this group to differ
from the hepatoma experience among alcoholics without
cirrhosis of the liver? (Hint: Use a 5% probability of getting
a result at least as extreme to denote differences between
the hepatoma experiences of the two groups.)
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