# 12 questions on correlation :

1. For each menu item at a fast food restaurant, fat content (in grams) and number of calories were recorded. A scatterplot of these data is given:

A plausible value for the correlation between calories and fat content is

A. – 0.9.

B. +0.2.

C. – 1.0.

D. +0.9.

2. The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

In this study, the explanatory variable is

A. the volume of oxygen consumed while running.

B. the measuring instrument used to measure the volume of oxygen consumed.

C. the volume of oxygen consumed at rest.

D. It doesn’t matte

3. Do taller restaurant servers receive larger tips? In a study, the amount of each tip (measured as a percentage of the bill) was recorded, along with the heights of the servers. The response variable is

A. the size of the tip.

B. the height of the server.

C. the number of servers used in the study.

D. None of the above

4. Which of the following statements is true?

A. The correlation coefficient equals the proportion of times two variables lie on a straight line.

B. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.

C. The correlation coefficient will be +1.0 only if all the data lie on a perfectly horizontal straight line.

D. The correlation coefficient measures the fraction of outliers that appear in a scatterplot.

5. A researcher measures the correlation between two variables. This correlation tells us

A. whether a scatterplot shows an interesting pattern.

B. whether there is a relation between two variables.

C. the strength and direction of a straight line relation between two variables.

D. whether a cause and effect relation exists between two variables.

6. If men always married women who were two years younger than themselves, the correlation between the ages of husband and wife would be

A. -1.

B. 1.

C. Can’t tell without seeing the data.

Each of the following statements contains a blunder. In each case, choose the statement that correctly explains the blunder.

7. “There is a high correlation between the sex of American workers and their income.”

A. Correlation requires both variables to be quantitative.

B. The correlation must give the units of the income.

C. The statement must include whether high income tracks with men or with women.

8. “We found a high correlation (r = 1.09) between students’ ratings of faculty teaching and ratings made by other faculty members.”

A. The correlation must be a number between -1 and 1.

B. The correlation must include the units of the ratings.

C. The correlati

9. “The correlation between height and weight of the subjects was r = 0.63 centimeter.”

A. The correlation has no unit of measurement; it is just a number.

B. The correlation must state which variable is the explanatory variable and which variable is the response variable.

C. Correlation can only measure a relationship between variables with the same units.

A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.”

The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.”

10. Which statement in plain language (i.e. without the word “correlation”) correctly explains the psychologist’s meaning?

A. While good researchers tend to be bad teachers, there is no similar relationship between bad researchers and good teachers.

B. Good researchers tend to be bad teachers and bad researches tend to be good teachers.

C. While bad researchers tend to be good teachers, there is no similar relationship between good researchers and bad teachers.

D. There is little connection between research productivity and teaching rating.

How sensitive to changes in water temperature are coral reefs? To find out, measure the growth of corals in aquariums where the water temperature is controlled at different levels. Growth is measured by weighing the coral before and after the experiment.

11. Select the correct statement.

A. The change in coral weight during the experiment is the explanatory variable, and the temperature of the aquarium is the response variable.

B. The change in coral weight during the experiment is the response variable, and the temperature of the aquarium is the explanatory variable.

C. The weight of the corals after the experiment is the response variable, and the temperature of the aquarium is the explanatory variable.

D. Growth of the coral will be used to determine an optimal temperature.

12. Temperature and weight are what kind of variables?

A. Both are numeric because they are both measured with instruments.

B. Temperature is categorical (cool, warm, or hot) and growth is numeric.

C. Both are categorical. We can classify growth as slow, medium, or fast. Temperatures are cool, warm, or hot.

D. Growth is categorical (slow, medium, or fast) and temperature is numeric because it is measured with a thermometer.

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