Question 1

Which of the following best describes the difference between a response variable and an explanatory variable in a statistical study?

Accepted Answer

A response variable measures the outcome of a study, while an explanatory variable may explain or influence changes in the response variable.

Question 2

In the context of the Titanic data, which of the following is a correct interpretation of a conditional proportion?

Accepted Answer

The proportion of first-class passengers who survived, out of all first-class passengers.

Question 3

Suppose you are analyzing a contingency table of smoking status (smoker/non-smoker) and disease status (disease/no disease). Which measure would you use to compare the likelihood of disease between smokers and non-smokers?

Accepted Answer

Odds ratio

Question 4

A segmented (stacked) bar chart is most useful for displaying:

Accepted Answer

Conditional distributions of one categorical variable within levels of another categorical variable.

Question 5

Given the following scenario: In a study, the amount of sleep (in hours) and test scores are recorded for a group of students. Which type of graph would be most appropriate to display the relationship between these two variables?

Accepted Answer

Scatterplot

Question 6

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient $$r$$ close to $$-1$$ indicates a strong negative linear relationship.

Question 7

Suppose you have the following data for two variables $$x$$ and $$y$$ for $$n$$ individuals: $$x_1$$, $$x_2$$, ..., x_n$$ and y_1$, y_2$, ..., y_n. $$Which formula correctly calculates the correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{1}{n-1} \sum_{i=1}^n \left( \frac{x_i - \bar{x}}{s_x} \right) \left( \frac{y_i - \bar{y}}{s_y} \right)$$

Question 8

A scatterplot of speed (km/hr) versus fuel consumption (liters/100 km) for a car shows a curved pattern. Which of the following is the best description of the relationship?

Accepted Answer

The relationship is non-linear (curved), so it does not make sense to describe it as simply positive or negative.

Question 9

In the sparrowhawk example, the number of new adults joining a colony and the percent of adults returning from the previous year are negatively associated. What is the most likely explanation for this negative association?

Accepted Answer

Returning adults claim territories, leaving less room for new recruits.

Question 10

Which of the following is NOT a correct interpretation of a marginal proportion in a contingency table?

Accepted Answer

The proportion of first-class survivors among all survivors.

Question 11

A researcher finds that the correlation between hours studied and exam score is $$r = 0.85. $$Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 12

Which of the following scenarios would be most appropriate for using a contingency table?

Accepted Answer

Examining the association between gender (male/female) and preference for a new product (like/dislike).

Question 13

If a scatterplot shows that as $$x$$ increases, $$y$$ tends to decrease, which of the following best describes the association?

Accepted Answer

Negative association

Question 14

Which of the following is a correct statement about the use of correlation?

Accepted Answer

Correlation is only appropriate for measuring linear relationships between two quantitative variables.

Question 15

A study finds that the odds of disease in smokers is $$0.3$$ and in non-smokers is $$0.1. $$What is the odds ratio of disease for smokers compared to non-smokers?

Accepted Answer

$$3.0$$

Question 16

Which of the following best describes a strong association in a scatterplot?

Accepted Answer

The points fall closely along a straight line.

Question 17

In a study of the effect of a new medication, patients are randomly assigned to receive either the medication or a placebo. The outcome is whether or not they recover. Which variable is the explanatory variable?

Accepted Answer

The type of treatment received (medication or placebo)

Question 18

Which of the following is a correct way to interpret a risk ratio (relative risk) of $$2.0$$ for disease in exposed versus unexposed groups?

Accepted Answer

The risk of disease is twice as high in the exposed group compared to the unexposed group.

Question 19

Which of the following is NOT a step in calculating the correlation coefficient $$r$$?

Accepted Answer

Sum the raw values of $$x$$ and $$y$$ for each observation.

Question 20

A researcher wants to know if there is an association between class (first, second, third, crew) and survival on the Titanic. Which statistical tool should they use to summarize the data?

Accepted Answer

Contingency table

Association: Contingency, Correlation, and Regression (Chapter 3 Study Notes)

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