Suppose we observe 84 alcoholics with cirrhosis of the liver, of whom 29 have hepatomas—that is, liver-cell carcenoma. Suppose we know, based on a large sample, that the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%. answer the following : 1. What is the probability that we observe exactly
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose we observe 84 alcoholics with cirrhosis of the liver, of whom 29 have hepatomas—that is, liver-cell carcenoma. Suppose we know, based on a large sample, that the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%.
answer the following :
1. 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?
2. What is the probability of observing at least 29 hepatomas among the 84 alcoholics with cirrhosis of the liver under the assumptions in Problem 1?
3. 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.)
1)
From the given information, n=80 and the probability of success is p=0.24(24%).
Normal Approximation to Binomial distribution:
If the random variable X follows Binomial(n, p), then the random variable X follows normal distribution by approximating µ as np and standard deviation as square root of np(1-p).
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