Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that relates two categories of data, with each cell representing a combination of categories.

Question 2

Given a contingency table with grades (A, B, C, D, F) as rows and delivery methods (Traditional, Online, Hybrid) as columns, what is the marginal distribution of grades?

Accepted Answer

The total frequency or relative frequency for each grade, summed across all delivery methods.

Question 3

How do you compute the relative frequency marginal distribution for a variable in a contingency table?

Accepted Answer

Sum the frequencies for each category of the variable and divide by the total number of observations.

Question 4

A professor finds that students in the hybrid course are more likely to pass (A, B, or C) than in traditional or online courses. What statistical concept is being used to make this observation?

Accepted Answer

Conditional distribution

Question 5

Which of the following is the correct formula for the conditional probability of event $$A$$ given event $$B$$?

Accepted Answer

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$

Question 6

Refer to the Titanic survival bar graph. Which demographic had the highest survival rate?

Accepted Answer

Women

Question 7

What does Simpson’s Paradox illustrate?

Accepted Answer

That the association between two variables can reverse or disappear when a third variable is considered.

Question 8

In the diabetes study, the overall proportion of Type 2 diabetics who died was $$\frac{218}{544} = 0.40. $$What is a possible lurking variable that could affect this result?

Accepted Answer

Age

Question 9

If the conditional probability of dying for Type 1 diabetics over 40 is $$\frac{104}{228} = 0.456$$ and for Type 2 diabetics over 40 is $$\frac{218}{529} = 0.412$$, what does this suggest about the lethality of the two types of diabetes for this age group?

Accepted Answer

Type 1 diabetes is more lethal for those over 40.

Question 10

Which of the following best describes a marginal distribution?

Accepted Answer

The distribution of one variable, ignoring the other variable in the contingency table.

Question 11

A conditional distribution is most useful for:

Accepted Answer

Identifying associations between two categorical variables.

Question 12

Suppose you observe Simpson’s Paradox in a dataset. What should you do before making a conclusion?

Accepted Answer

Investigate whether a lurking variable is influencing the observed association.

Question 13

Which of the following is NOT a characteristic of a contingency table?

Accepted Answer

It only displays numerical data.

Question 14

If the marginal distribution of grades shows that 40% of students received a C, what does this mean?

Accepted Answer

40% of students received a C, regardless of delivery method.

Question 15

Which of the following is an example of a conditional distribution?

Accepted Answer

The proportion of students who received an A in the hybrid course.

Question 16

A bar graph shows that the relative frequency of survival for women on the Titanic is higher than for men. What type of distribution is being displayed?

Accepted Answer

Conditional distribution of survival status by demographic.

Question 17

Which of the following best explains why the overall death rate for Type 2 diabetics appears higher than for Type 1 diabetics, but this reverses when age is considered?

Accepted Answer

Simpson’s Paradox, due to age acting as a lurking variable.

Contingency Tables, Association, and Simpson’s Paradox in Introductory Statistics

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