Question 1

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

Accepted Answer

The response variable is the outcome variable on which comparisons are made, while the explanatory variable defines the groups to be compared with respect to values on the response variable.

Question 2

In a study examining the association between the number of hours studied and the grade on a test, which is the explanatory variable?

Accepted Answer

Number of hours studied

Question 3

Which of the following statements best defines an association between two variables?

Accepted Answer

An association exists if a particular value for one variable is more likely to occur with certain values of the other variable.

Question 4

A contingency table is used to:

Accepted Answer

Display the frequencies of two categorical variables.

Question 5

Given the following contingency table for food type and pesticide status, what is the response variable?

| Food Type | Pesticide Present | Pesticide Not Present | Total |
|-----------|-------------------|----------------------|-------|
| Organic   | 29                | 98                   | 127   |
| Conventional | 19485           | 7086                 | 26571 |
| Total     | 19514             | 7184                 | 26698 |

Accepted Answer

Pesticide Status

Question 6

How do you calculate the conditional proportion of organic foods that contain pesticides using the table below?

| Food Type | Pesticide Present | Pesticide Not Present | Total |
|-----------|-------------------|----------------------|-------|
| Organic   | 29                | 98                   | 127   |
| Conventional | 19485           | 7086                 | 26571 |
| Total     | 19514             | 7184                 | 26698 |

Accepted Answer

$\frac{29}{127}$

Question 7

If there is no association between food type (organic vs. conventional) and pesticide status (present vs. not present), what would you expect about the conditional proportions of pesticide presence for each food type?

Accepted Answer

They would be the same for each food type.

Question 8

Which graphical display is most appropriate for visualizing the association between two quantitative variables?

Accepted Answer

Scatterplot

Question 9

A scatterplot shows a strong positive linear relationship between two variables. Which of the following is most likely true about the correlation coefficient $r$?

Accepted Answer

$r$ is close to +1

Question 10

Which of the following is NOT a property of the correlation coefficient $r$?

Accepted Answer

$r$ is resistant to outliers

Question 11

Suppose you have the following data for two variables $x$ and $y$:

$x$: 2, 4, 6, 8
$y$: 3, 6, 9, 12

What is the value of the correlation coefficient $r$?

Accepted Answer

$r = 1$

Question 12

Which of the following scenarios is most likely to produce a negative association in a scatterplot?

Accepted Answer

Age of a car and its resale value

Question 13

Which formula is used to calculate the correlation coefficient $r$ for a sample of $n$ paired data $(x_i, y_i)$?

Accepted Answer

$r = \frac{1}{n-1} \sum \left( \frac{x_i - \overline{x}}{s_x} \right) \left( \frac{y_i - \overline{y}}{s_y} \right)$

Question 14

Which of the following statements about correlation is TRUE?

Accepted Answer

Correlation is affected by outliers.

Question 15

A scatterplot of two variables shows a cloud of points with no discernible pattern or direction. What can you conclude about the correlation coefficient $r$?

Accepted Answer

$r$ is close to 0

Question 16

If you change the units of measurement for one or both variables (for example, from inches to centimeters), what happens to the value of the correlation coefficient $r$?

Accepted Answer

It remains unchanged

Question 17

Which of the following is an example where a contingency table would be appropriate?

Accepted Answer

Comparing the relationship between gender (male/female) and smoking status (smoker/non-smoker)

Question 18

A researcher finds that the correlation between two variables is $r = 0.95$. Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear association between the two variables.

Question 19

Which of the following is a potential consequence of an outlier in a data set when calculating the correlation coefficient?

Accepted Answer

The correlation coefficient may be greatly increased or decreased.

Association Between Two Categorical Variables: Contingency Tables and Proportions

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