Q: In a study, 124 out of 6272 men never/seldom ate fish, and 14 of them developed prostate cancer. What is the percentage of prostate cancer in this group?

$$ \frac{14}{124} \times 100 \approx 11.3\% $$

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 their counts or frequencies.

Question 2

In a contingency table, what is a marginal distribution?

Accepted Answer

The distribution of one variable across all categories of the other variable.

Question 3

Suppose a contingency table shows pet ownership by gender. If 6.3% of OkCupid pet owners are women who have both a dog and a cat, what type of percentage is this?

Accepted Answer

Joint percentage

Question 4

Given the following counts from a study: 41 right-side sleepers, 22 left-side sleepers; 6 right-side sleepers had nightmares, 9 left-side sleepers had nightmares. What is the conditional probability that a left-side sleeper had nightmares?

Accepted Answer

$$ \frac{9}{22} $$

Question 5

Which graphical display is most appropriate for visualizing the relationship between three categorical variables?

Accepted Answer

Mosaic plot

Question 6

In the context of the Titanic data, which percentage answers the question: 'Of the survivors, what group was most common?'

Accepted Answer

Column percentage

Question 7

If the distribution of one variable is the same for all categories of another variable, what can be concluded?

Accepted Answer

The variables are independent.

Question 8

A study finds that 7.4% of Swedish men developed prostate cancer. If 11.3% of men who never/seldom ate fish developed prostate cancer, what does this suggest?

Accepted Answer

Fish consumption may be associated with a lower risk of prostate cancer.

Question 9

Which of the following is an example of Simpson’s Paradox?

Accepted Answer

A trend that appears in several groups of data but disappears or reverses when the groups are combined.

Question 10

In the Berkeley admissions case, why did women appear to be discriminated against when looking at overall admission rates?

Accepted Answer

Women applied in larger numbers to schools with lower admission rates, which was a lurking variable not considered in the overall rates.

Question 11

Which of the following is a lurking variable in the context of the Berkeley admissions example?

Accepted Answer

School applied to

Question 12

If you want to compare the percentage of men and women who plan to watch the Super Bowl, which type of percentage should you use?

Accepted Answer

Row percentage

Question 13

A bar chart is used to display conditional distributions. What is a potential drawback of using pie charts instead?

Accepted Answer

Pie charts make it difficult to be precise about comparisons.

Question 14

Which of the following is NOT a recommended practice when analyzing contingency tables?

Accepted Answer

Ignore lurking variables.

Question 15

Suppose you have the following data: 100 flights during the day, 20 flights at night. 90 day flights were on time, 10 night flights were on time. What is the overall on-time percentage?

Accepted Answer

$$ \frac{90 + 10}{100 + 20} = \frac{100}{120} = 83.3\% $$

Question 16

Why can combining results across groups sometimes lead to misleading conclusions?

Accepted Answer

Different group sizes and distributions can mask or reverse trends present within groups.

Question 17

In a study, 124 out of 6272 men never/seldom ate fish, and 14 of them developed prostate cancer. What is the percentage of prostate cancer in this group?

Accepted Answer

$$ \frac{14}{124} 	imes 100 \approx 11.3\% $$

Question 18

Which of the following best describes an observational study?

Accepted Answer

A study where researchers observe and record data without manipulating variables.

Question 19

If you want to know the percentage of first-class passengers who survived the Titanic, which formula would you use?

Accepted Answer

$$ \frac{	ext{Number of first-class survivors}}{	ext{Total number of first-class passengers}} 	imes 100 $$

Chapter 3: Relationships Between Categorical Variables – Contingency Tables

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