Q: Suppose you want to know the percentage of third-class passengers who survived the Titanic. Which calculation is correct?

$$\frac{181}{709} \times 100\%$$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that shows the relationship between two categorical variables by displaying counts for each combination of categories.

Question 2

Given the Titanic contingency table, what is the marginal distribution of Survival?

Accepted Answer

$$\frac{712}{2208}$$ survived, $$\frac{1496}{2208}$$ died

Question 3

What is the conditional distribution of Survival for crew members on the Titanic?

Accepted Answer

$$\frac{212}{891}$$ survived, $$\frac{679}{891}$$ died

Question 4

If the conditional distribution of one variable is the same for all categories of another variable, what can we conclude?

Accepted Answer

The variables are independent.

Question 5

Which graphical display is most appropriate for visualizing the conditional distribution of ticket class among Titanic survivors?

Accepted Answer

Segmented bar chart

Question 6

What does a mosaic plot add to a segmented bar chart when displaying a contingency table?

Accepted Answer

It uses bar widths proportional to the frequencies in the category on the horizontal axis.

Question 7

Suppose you want to know the percentage of third-class passengers who survived the Titanic. Which calculation is correct?

Accepted Answer

$$\frac{181}{709} 	imes 100\%$$

Question 8

Which of the following statements is supported by the Titanic data?

Accepted Answer

There is an association between survival and class.

Question 9

What is the marginal distribution of ticket class among all Titanic passengers?

Accepted Answer

$$\frac{324}{2208}$$ first, $$\frac{284}{2208}$$ second, $$\frac{709}{2208}$$ third, $$\frac{891}{2208}$$ crew

Question 10

If you switch the variables on the axes of a mosaic plot, what changes?

Accepted Answer

The interpretation and visual emphasis of the association between the variables.

Question 11

A segmented bar chart shows that the proportion of crew members who died is much higher than the proportion of first-class passengers who died. What does this suggest?

Accepted Answer

There is an association between class and survival.

Question 12

Which of the following is a marginal distribution?

Accepted Answer

The distribution of survival status for all passengers.

Question 13

What percent of crew members survived the Titanic disaster?

Accepted Answer

$$\frac{212}{891} 	imes 100\% \approx 23.8\%$$

Question 14

Which of the following best describes a conditional distribution?

Accepted Answer

The distribution of one variable for individuals who satisfy a condition on another variable.

Question 15

If the conditional distribution of survival is different for each class, what does this indicate?

Accepted Answer

Survival and class are associated.

Question 16

Which of the following is NOT a valid way to display the relationship between two categorical variables?

Accepted Answer

Histogram

Question 17

In the context of the Titanic data, what does the term 'marginal distribution' refer to?

Accepted Answer

The distribution of a single variable, such as survival or class, across all passengers.

Question 18

Which of the following best describes the difference between a segmented bar chart and a mosaic plot?

Accepted Answer

A mosaic plot uses bar widths proportional to category frequencies, while a segmented bar chart does not.

Relationships Between Categorical Variables: Contingency Tables and Graphical Displays

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