A researcher says that there is a 78% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 5% chance that the polygraph will falsely accuse someone of lying. (a) If the polygraph indicated that 35% of the questions were answered with lies, what would you estimate for the actual percentage of lies in the answers? Hint: Let B = event detector indicates a lie. We are given P(B) = 0.35. Let A = event person is lying, so Ac = event person is not lying. Then P(B) = P(A and B) + P(Ac and B) P(B) = P(A)P(B | A) + P(Ac)P(B | Ac) Replacing P(Ac) by 1 − P(A) gives P(B) = P(A) · P(B | A) + [1 − P(A)] · P(B | Ac) Substitute known values for P(B), P(B | A), and P(B | Ac) into the last equation and solve for P(A). (Round your answer to two decimal places.) P(A) = (b) If the polygraph indicated that 65% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.) %
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.
A researcher says that there is a 78% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 5% chance that the polygraph will falsely accuse someone of lying.
P(B) = P(A)P(B | A) + P(Ac)P(B | Ac)
P(A) =
(b) If the polygraph indicated that 65% of the questions were answered with lies, what would you estimate for the actual percentage of lies? (Round your answer to one decimal place.)
%
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