Q: In the Titanic data, what percent of Third Class passengers survived?

$$\frac{181}{709} \times 100 \approx 25.5\%$$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

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

Question 2

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

Accepted Answer

$$\frac{712}{2208}$$ Alive, $$\frac{1496}{2208}$$ Dead

Question 3

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

Accepted Answer

$$\frac{212}{891}$$ Alive, $$\frac{679}{891}$$ Dead

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 two 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

In the Titanic data, what percent of Third Class passengers survived?

Accepted Answer

$$\frac{181}{709} 	imes 100 \approx 25.5\%$$

Question 7

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

Accepted Answer

Survival and Class are associated because the distribution of Class among survivors is different from that among non-survivors.

Question 8

What is the main difference between a segmented bar chart and a mosaic plot?

Accepted Answer

A mosaic plot has bar widths proportional to the frequencies in the category on the horizontal axis.

Question 9

Suppose you want to compare the distribution of Survival for each Class on the Titanic. Which display would best help you see if Survival is associated with Class?

Accepted Answer

Mosaic plot with Class on the horizontal axis and Survival on the vertical axis

Question 10

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

Accepted Answer

The arrangement of the bars, which may make patterns of association easier or harder to see.

Question 11

Given the Titanic data, what is the probability that a randomly selected passenger was Crew and survived?

Accepted Answer

$$\frac{212}{2208}$$

Question 12

Which of the following is a marginal distribution from the Titanic contingency table?

Accepted Answer

$$\frac{324}{2208}$$ First Class

Question 13

If the conditional distribution of Survival for each Class is different, what does this suggest?

Accepted Answer

There is an association between Survival and Class.

Question 14

A segmented bar chart shows that the proportion of Crew who died is much higher than the proportion of First Class who died. What does this indicate?

Accepted Answer

There is a relationship between Class and Survival.

Question 15

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

Accepted Answer

Scatterplot

Question 16

If 28.2% of survivors were in First Class, how many survivors were in First Class?

Accepted Answer

$$0.282 	imes 712 = 201$$

Question 17

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 18

In a real-world scenario, why might you use a mosaic plot instead of a segmented bar chart?

Accepted Answer

To show both the proportion and the actual frequency of categories on the horizontal axis.

Relationships Between Categorical Variables: Contingency Tables and Graphical Displays

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