Q: Using the same contingency table, what percentage of individuals with a low cholesterol diet have coronary heart disease?

$$\frac{2}{8} \times 100\% = 25\%$$

Question 1

Which of the following best describes a relative frequency table for categorical data?

Accepted Answer

A table that lists all categories and their frequencies as percentages or proportions, with the total adding up to 100%.

Question 2

A bar chart is used to display which type of data, and how are the bars represented?

Accepted Answer

Categorical data; bars have equal width and their heights represent frequency or relative frequency.

Question 3

In a pie chart, what does the area of each slice represent?

Accepted Answer

The fraction of the whole for the category it represents.

Question 4

Given the following contingency table for 23 individuals:

$$\begin{array}{l|cc|c}
& 	ext{Yes} & 	ext{No} & 	ext{Total} \
\hline
	ext{High cholesterol diet} & 11 & 4 & 15 \
	ext{Low cholesterol diet} & 2 & 6 & 8 \
\hline
	ext{Total} & 13 & 10 & 23 \
\end{array}$$

What is the marginal distribution of diet type?

Accepted Answer

High cholesterol diet: $$\frac{15}{23} = 65.2\%$$, Low cholesterol diet: $$\frac{8}{23} = 34.8\%$$

Question 5

Using the same contingency table, what percentage of individuals with a low cholesterol diet have coronary heart disease?

Accepted Answer

$$\frac{2}{8} 	imes 100\% = 25\%$$

Question 6

What is a conditional distribution in the context of a contingency table?

Accepted Answer

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

Question 7

If 73.3% of individuals with a high cholesterol diet have heart disease, and only 25% of those with a low cholesterol diet have heart disease, what can you conclude about the relationship between diet type and heart disease?

Accepted Answer

Diet type and presence of coronary heart disease are associated.

Question 8

Which of the following best describes Simpson's Paradox?

Accepted Answer

A phenomenon where the direction of association between two categorical variables reverses when accounting for a third variable.

Question 9

A hospital advertises a lower overall rate of delayed discharge (10%) compared to a larger hospital (13%). However, when broken down by surgery type, the small hospital has higher rates for both major and minor surgeries. What statistical phenomenon does this illustrate?

Accepted Answer

Simpson's Paradox

Question 10

Given a segmented bar chart showing the presence of coronary heart disease by diet type, what does each segment within a bar represent?

Accepted Answer

A category of a second categorical variable, with area proportional to its fraction within the bar's group.

Question 11

If you want to compare the distribution of a single categorical variable across several groups, which graphical display is most appropriate?

Accepted Answer

Segmented bar chart

Question 12

In a contingency table, what is the grand total?

Accepted Answer

The sum of all frequencies in the table.

Question 13

A study finds that 84.6% of individuals with coronary heart disease have a high cholesterol diet. What type of distribution is this?

Accepted Answer

Conditional distribution (conditioned on having heart disease)

Question 14

Which of the following is NOT a correct property of a relative frequency table for non-overlapping categories?

Accepted Answer

The percentages may add up to more than 100%.

Question 15

Suppose you have the following data: 13 individuals have heart disease, and 10 do not, out of 23 total. What is the relative frequency of individuals without heart disease?

Accepted Answer

$$\frac{10}{23} \approx 43.5\%$$

Question 16

Which of the following best describes a marginal distribution in a contingency table?

Accepted Answer

The distribution of totals for one variable, summing over the levels of the other variable.

Question 17

A pie chart is most appropriate for which of the following scenarios?

Accepted Answer

Displaying the proportion of students in different majors at a university.

Question 18

If a bar chart is constructed for the city of residence of 30-day transit riders, and Vancouver has a bar reaching 39% on the y-axis, what does this indicate?

Accepted Answer

39% of the sample of 30-day transit riders reside in Vancouver.

Question 19

Which of the following statements about Simpson's Paradox is TRUE?

Accepted Answer

It can occur when a third variable influences the association between two variables, reversing the observed relationship.

Displaying Categorical Data in Statistics

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