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 of each grade across all delivery methods.

Question 3

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

Accepted Answer

Divide the frequency of each category by the total number of observations.

Question 4

A professor finds that 40% of students in a hybrid course received a grade of C, while only 25% of students in a traditional course received a C. What type of distribution is being described?

Accepted Answer

Conditional distribution

Question 5

Which of the following is true about conditional distributions?

Accepted Answer

They list the relative frequency of each category of the response variable, given a specific value of the explanatory variable.

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 change or reverse when a third variable is considered.

Question 8

In a study, the proportion of patients with Type 1 diabetes who died was $$\frac{105}{358} = 0.29$$, and for Type 2 diabetes it was $$\frac{218}{544} = 0.40. $$What might you incorrectly conclude if you ignore age?

Accepted Answer

Type 2 diabetes is more lethal than Type 1 diabetes.

Question 9

After accounting for age, the proportion of patients over 40 who died was $$\frac{104}{228} = 0.456$$ for Type 1 and $$\frac{218}{529} = 0.412$$ for Type 2. What does this reveal about the initial conclusion?

Accepted Answer

The association between diabetes type and lethality reversed when age was considered.

Question 10

Which of the following best describes a lurking variable?

Accepted Answer

A variable that affects the association between two other variables but is not included in the analysis.

Question 11

Suppose you are analyzing the effectiveness of three teaching methods using a contingency table. What would be the best way to determine if there is an association between teaching method and student grade?

Accepted Answer

Compare the conditional distributions of grades for each teaching method.

Question 12

If the conditional distribution of survival status by demographic on the Titanic shows that women had a higher survival rate than men, what does this suggest?

Accepted Answer

There is an association between demographic and survival.

Question 13

Which formula would you use to calculate the proportion of a category in a conditional distribution?

Accepted Answer

$$\frac{	ext{Frequency of category}}{	ext{Total for given condition}}$$

Question 14

A bar graph shows that the relative frequency of students earning a C is highest in the hybrid course. What can you infer?

Accepted Answer

Students in hybrid courses are more likely to earn a C compared to other methods.

Question 15

Which of the following is NOT a possible reason for Simpson’s Paradox to occur?

Accepted Answer

There is a strong association between two variables that remains unchanged when a third variable is introduced.

Ch 4 part 2 Contingency Tables and Association

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