Consider estimating a population proportion of “successes” p. The natural estimator of p is the sample proportion of successes p ˆ . The number of successes X in the sample has a binomial distribution with parameters n and p. It is known that p ˆ is an unbiased estimator of p. Is 2 p ˆ an unbiased estimator of 2 p ? Show all steps.
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.
Consider estimating a population proportion of “successes” p. The natural estimator of p is the
sample proportion of successes
p
ˆ
. The number of successes X in the sample has a binomial
distribution with parameters n and p. It is known that
p
ˆ
is an unbiased estimator of p. Is
2
p
ˆ
an
unbiased estimator of
2
p
? Show all steps.
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