A multiple-choice exam consists of 50 questions. Each question has five choices, of which only one is correct. Suppose that the total score on the exam is computed as where x1 = number of correct responses and x2 = number of incorrect responses. (Calculating a total score by subtracting a term based on the number of incorrect responses is known as a correction for guessing and is designed to discourage test takers from choosing answers at random.) a. It can be shown that if a totally unprepared student answers all 50 questions by just selecting one of the five answers at random, then µx1 = 10 and µx2 = 40. What is the mean value of the total score, y? Does this surprise you? Explain. b. Explain why it is unreasonable to use the formulas given in this section to compute the variance or standard deviation of y.
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 multiple-choice exam consists of 50 questions. Each question has five choices, of which only one is correct. Suppose that the total score on the exam is computed as
where x1 = number of correct responses and x2 = number of incorrect responses. (Calculating a total score by subtracting a term based on the number of incorrect responses is known as a correction for guessing and is designed to discourage test takers from choosing answers at random.)
a. It can be shown that if a totally unprepared student answers all 50 questions by just selecting one of the five answers at random, then µx1 = 10 and µx2 = 40. What is the mean value of the total score, y? Does this surprise you? Explain.
b. Explain why it is unreasonable to use the formulas given in this section to compute the variance or standard deviation of y.
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