AnswersDRHS GA-Statistical ReasoningCorrelation

Correlation Answers

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A scatterplot shows the relationship between semester tuition and 4-year graduation rate for several colleges. The graph shows that as tuition increases, graduation rates also tend to increase.

Question illustration
A
Higher tuition causes students to graduate at higher rates.
B
Graduation rate causes tuition to increase at colleges.
C
There is no relationship between tuition and graduation rate.
D
There is a positive association between tuition and graduation rate, but this does not mean one causes the other.
2
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Fuel efficiency, measured in miles per gallon, is a feature often considered by shoppers looking for a new car. The scatterplot shows the vehicle weight of 15 car models in pounds, plotted against their highway fuel efficiency.

Question illustration
A
–0.197
B
–0.898
C
0.528
D
0.902
3

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856.

Question illustration
A
The correlation would stay the same.
B
The correlation would stay positive and increase.
C
The correlation would stay positive and decrease.
D
The correlation would be negative, rather than positive.
4

A health organization collects data on hospitals in a large metropolitan area. The scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay).

Question illustration
A
the hospital with 35 beds
B
the hospital with 140 beds
C
the hospital with 200 beds
D
the hospital with 310 beds
5

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. Which of the following is a correct interpretation of this value?

A
Each additional calorie is predicted to add approximately 0.83 mg of sodium.
B
There is a positive relationship between calories and sodium. The relationship is weak.
C
There is a positive relationship between calories and sodium. The relationship is strong.
D
As the number of calories increases, the amount of sodium decreases. The relationship is strong.
6

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856.

Question illustration
A
There is no relationship between tuition and graduation rate.
B
Colleges with lower tuition tend to have higher graduation rates.
C
Colleges with higher tuition tend to have higher graduation rates.
D
There is a weak, positive relationship between tuition and graduation rate.
7

An entertainment reporter examines the average ticket prices of Broadway shows, comparing them to the number of total performances the shows have had. A resulting scatterplot shows a strong, positive relationship. The value of r for the scatterplot is 0.763. Which statement best explains the relationship between the variables?

A
Lower ticket prices cause fewer performances to be offered.
B
Higher ticket prices cause more performances to be offered.
C
Less popular shows have higher ticket prices and offer fewer performances.
D
More popular shows have higher ticket prices and offer more performances.
8

An official for a regional baseball league examines attendance data for teams in the league. For each team in the league, the number of losses and the average game attendance are shown in the scatterplot. The value of r for the scatterplot is –0.847.

Question illustration
A
There is no association between losses and attendance.
B
Losses and attendance have a strong, positive association.
C
Losses and attendance have a weak, negative association.
D
Losses and attendance have a strong, negative association.
9

An economist studies the relationship between the unemployment rate of adult males and male life expectancy for 12 European countries. The relationship is shown in the scatterplot. The value of r for the scatterplot is –0.423.

Question illustration
A
Unemployment is a cause of lower life expectancy.
B
Countries with higher unemployment rates also have higher life expectancy.
C
Lower unemployment rates may have an association with unhealthy lifestyles, which is also associated with lower life expectancy.
D
Higher unemployment rates may have an association with unhealthy lifestyles, which is also associated with lower life expectancy.
10

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car’s stopping distance, in feet, for each volunteer.

Question illustration
A
reaction time 0.5 seconds, stopping distance 35 feet
B
reaction time 1.7 seconds, stopping distance 53 feet
C
reaction time 2 seconds, stopping distance 67 feet
D
reaction time 2.1 seconds, stopping distance 60 feet

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