Question 1

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

Accepted Answer

The response variable is the outcome measured, while the explanatory variable defines the groups to be compared.

Question 2

Given the contingency table below, what is the conditional proportion of organic foods that contain pesticides?

Organic: 29 (Yes), 98 (No), Total = 127

Accepted Answer

$$\frac{29}{127} = 0.23$$

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 displays which type of data?

Accepted Answer

Two categorical variables

Question 5

Suppose you want to compare the proportion of foods with pesticides between organic and conventional types. Which statistical tool would you use?

Accepted Answer

Contingency table and conditional proportions

Question 6

If there is no association between food type (organic/conventional) and pesticide presence, what would you expect about the conditional proportions?

Accepted Answer

The conditional proportions for pesticide presence would be the same for both food types.

Question 7

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

Accepted Answer

$$r$$ depends on the units of the variables.

Question 8

Given the formula for the correlation coefficient:

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

What does a value of $$r = 0$$ indicate?

Accepted Answer

There is no linear relationship between the variables.

Question 9

Which of the following scenarios would most likely show a negative association in a scatterplot?

Accepted Answer

Age of a car and its resale value

Question 10

A scatterplot of pulse rate (y) versus time to swim 2000 yards (x) shows a downward trend. What does this indicate about the association?

Accepted Answer

There is a negative association: as time increases, pulse rate decreases.

Question 11

Which of the following best describes the effect of an outlier on the correlation coefficient $$r$$?

Accepted Answer

Outliers can greatly increase or decrease the value of $$r.$$

Question 12

Which of the following is a correct interpretation of a correlation coefficient $$r = 0.89$$ between internet usage and GDP for a set of countries?

Accepted Answer

There is a strong positive linear association between internet usage and GDP.

Question 13

Why can correlation only be used to describe the association between two quantitative variables?

Accepted Answer

Because categorical variables do not have means and standard deviations.

Question 14

Suppose the correlation between the age of husbands and wives is $$r = 1. $$What does this mean?

Accepted Answer

There is a perfect positive linear relationship between the ages.

Question 15

Which of the following best describes a strong linear relationship in a scatterplot?

Accepted Answer

The points closely follow a straight line.

Question 16

If you switch the explanatory and response variables in a correlation calculation, what happens to the value of $$r$$?

Accepted Answer

The value of $$r$$ remains the same.

Question 17

A researcher finds that the correlation between two variables is $$r = -0.91. $$Which of the following is the best interpretation?

Accepted Answer

There is a strong negative linear association between the variables.

Question 18

Which of the following is a correct way to calculate the overall proportion of foods containing pesticides in the sample?

(Use the totals from the contingency table: 19514 foods with pesticides out of 26698 total foods.)

Accepted Answer

$$\frac{19514}{26698}$$

Question 19

Which of the following is NOT a reason why a tight fit to a horizontal line in a scatterplot does NOT imply a strong correlation?

Accepted Answer

A tight fit to a horizontal line means $$r is $$close to $$+1 or$$ $$-1.$$

Association: Contingency, Correlation, and Regression – Study Notes

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