Independent Variables and Two-Way Tables
Numbers sitting in a little table seem easy enough, but you’d be surprised at all the information you can get out of a table, and how many equations, formulas, and notations that you can squeeze out of them. Solve the following problems about independent variables and two-way tables.
If variables A and B are independent, which of the following must be true?
A. P(A) = P(B)
B. P(A) does not equal P(B)
C. P(A) does not depend on whether or not B occurs.
D. P(A) depends on P(B).
E. Choices (A) and (C)
Answer: C. P(A) does not depend on whether or not B occurs.
The question states that the variables A and B are independent. Two variables are independent if the probability of one event occurring doesn’t depend on whether the other event occurs; therefore, their probabilities aren’t affected by the occurrence of the other event.
Suppose that in a population of high-school seniors, the choice to enroll in higher education after graduation is independent of gender. Which of the following statements would be true?
A. The same number of males and females choose to enroll in higher education.
B. The same proportion of males and females choose to enroll in higher education.
C. More males enlist in the military, and more females go directly to full-time work.
D. Choices (B) and (C)
E. None of the above.
Answer: B. The same proportion of males and females choose to enroll in higher education.
Note that although the same proportion of males and females will choose to enroll, it may not be true that the same number of males and females choose to enroll, because the senior class may not have the same number of males and females.
A small town has 300 male registered voters and 350 female registered voters. Overall, 60% of voters voted for a bond initiative. If voting is independent of gender in this sample, how many women voted for the bond initiative?
Given this data, if 60% of voters voted for the bond initiative and voting was independent of gender, you’d also expect 60% of female voters to vote for the bond initiative. To find the expected number of women who voted for the bond initiative, you multiply the total number of female registered voters by 60%: 350(0.6) = 210.
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