Deck 7: Correlation and Causality

Question 1

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A)-0.65
B)0.95
C)0.65
D)0.20

Answer 1

C

Question 2

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-The age of a car and its fuel efficiency.

A)Positive correlation
B)Negative correlation
C)Not correlated

Answer 2

Negative correlation

Question 3

State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause.

- For a group of students in a statistics class, the scatter diagram compares their test scores (y)and the amount of loose pocket change they have(x).

A)Negative correlation; direct cause
B)Negative correlation; coincidence
C)No correlation
D)Negative correlation; common underlying cause

Answer 3

Negative correlation; coincidence

Question 4

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A)0.9
B)-0.6
C)-0.1
D)0.6

Question 5

Solve the problem.

-The table below shows the times (in hours)that seven students spend watching television and using the internet. Construct a scatter diagram for the data and state whether these times have no correlation, a positive correlation, or a negative correlation.

$\begin{array}{l}\text { Student TV TimeInternet Time }\\\begin{array}{lcc} & \text { (hours) } & \text { (hours) } \\\text { Tom } & 9 & 6 \\\text { Dick } & 5 & 4 \\\text { Harry } & 3 & 0 \\\text { Sue } & 8 & 9 \\\text { Betty } & 8 & 10 \\\text { Erin } & 6 & 1 \\\text { Jan } & 7 & 10\end{array}\end{array}$

A) Negative correlation


B) Positive correlation


C) No correlation



D) Positive correlation

Question 6

State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause.

- For several customers at the local bookstore, the scatter diagram compares the weight of their books (y)and the umber of pages in them(x).

A)Positive correlation; coincidence
B)Positive correlation; direct cause
C)No correlation
D)Negative correlation; common underlying cause

Question 7

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-Rate of pedaling a bicycle and speed of the bicycle

A)Positive correlation
B)Negative correlation
C)Not correlated

Question 8

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-The age of a textbook and how well it is written

A)Positive correlation
B)Negative correlation
C)Not correlated

Question 9

Solve the problem.

-The table below shows the legal costs and the profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether legal costs and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.


$\begin{array} { c c c } & \text { Legal Costs } & \text { Profits } \\\text { Year } & \text { (Millions of \$) } & \text { (Millions of \$) } \\2000 & 9 & 9 \\2001 & 14 & 6 \\2002 & 12 & 8 \\2003 & 11 & 14 \\2004 & 15 & 9 \\2005 & 10 & 15\end{array}$

A) Positive correlation


B) Positive correlation


C) No correlation


D) Negative correlation

Question 10

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-Time spent walking and distance covered

A)Positive correlation
B)Negative correlation
C)Not correlated

Question 11

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A)-0.1
B)-0.9
C)-0.5
D)0.9

Question 12

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A)0.9
B)-0.9
C)0.5
D)-0.5

Question 13

Provide an appropriate response.
Estimate the coordinates of the outlier on the graph.

Question 14

State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause.

- For a group of employees at the local video store, the scatter diagram compares the number of days worked per year (y)and the average number of miles walkedweekly (x).

A)Positive correlation; coincidence
B)No correlation
C)Positive correlation; direct cause
D)Positive correlation; common underlying cause

Question 15

State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause.

- For a group of English students at the local junior college, the scatter diagram compares the number of correct answers on a test they took(y)and the length of the pencil used to take the test(x).

A)Positive correlation; direct cause
B)Negative correlation; coincidence
C)No correlation
D)Positive correlation; coincidence

Question 16

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-The number of hours one sleeps and the number of hours one is awake

A)Positive correlation
B)Negative correlation
C)Not correlated

Question 17

State whether you believe the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative.

-The time it takes to read a book and the length of the book

A)Positive correlation
B)Negative correlation
C)Not correlated

Question 18

Solve the problem.

-The following table gives the total sales (revenue)and profits for 8 retailers. Construct a scatter diagram for thedata and state whether sales and profits for these companies have no correlation, a positive correlation, or a
Negative correlation.

$\begin{array}{l}\begin{array} { l c c } \hline \text { Company } & \begin{array} { c } \text { Total Sales } \\\text { (Millions of \$) }\end{array} & \begin{array} { c } \text { Profits } \\\text { (Millions of \$) }\end{array} \\\hline \text { Adams } & 9.5 & 0.5 \\\text { Browns } & 22.0 & 1.4 \\\text { Clay } & 35.0 & 1.8 \\\text { Donners } & 64.0 & 3.0 \\\text { Esters } & 27.5 & 0.9 \\\text { Framer } & 45.0 & 2.6 \\\text { Gillies } & 15.0 & 0.8 \\\text { Hays } & 57.0 & 2.2 \\\hline\end{array}\\\end{array}$

A) Positive correlation


B) Negative correlation


C) Positive correlation


D) No correlation

Question 19

How does the outlier affect the correlation coefficient?.

A)The outlier has no effect on the correlation coefficient.
B)The outlier reduces the correlation coefficient.
C)The outlier increases the correlation coefficient.
D)None of the above

Question 20

Solve the problem.

-The table below shows the sales and profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether sales and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.

$\begin{array} { c c c } \text { Year } & \text { (Millions of \$) } & \begin{array} { c } \text { Profits } \\\text { (Millions of \$) }\end{array} \\2000 & 7 & 1 \\2001 & 12 & 4 \\2002 & 10 & 2 \\2003 & 9 & 2 \\2004 & 13 & 3 \\2005 & 8 & 0\end{array}$

A) Negative correlation


B) Positive correlation


C) No correlation


D) No correlation

Question 21

Solve the problem. Round your answers to the nearest whole percent.
end

Question 22

Write the coordinates of a point that would be an outlier on the following graph.

A)(23, 20)
B)(6, 5)
C)(20, 0)
D)(12, 10)

Question 23

To get the best deal on a microwave oven, Amanda called six appliance stores and asked the cost and volume of several models. The prices and volumes she was quoted are listed below. Amanda later learned that the group of 3 microwaves with volumes greater than 1 cubic foot and costing less than $200 were discontinued models Priced lower than normal. How does this change your view of the correlation? $$\begin{array} { c c } \hline \text { Volume (cu.ft) } & \text { Price } ( \$ ) \\\hline 1.5 & 17 \\0.7 & 49 \\1.5 & 349 \\1.9 & 183 \\0.5 & 119 \\2.2 & 119 \\1.8 & 417 \\1.5 & 463 \\1 & 200 \\\hline\end{array}$$

A)Within each of the two groups, the correlation is less than it is overall.
B)The group of discontinued models has a stronger correlation than the other group.
C)There is little correlation either within the groups or overall.
D)Within each of the two groups, the correlation is stronger than it is overall.

Question 24

The table contains the weights (in pounds)and heights (in inches)of 9 randomly selected adults. Construct a scatter diagram for the data.

$$\begin{array}{l}\begin{array} { c c } \hline \text { Weight (lb)}&\text { Height (in.) } \\ \hline 125 & 60 \\130 & 62 \\128 & 70 \\130 & 65 \\155 & 75 \\150 & 72 \\135 & 68 \\145 & 68 \\145 & 65 \\\hline\end{array}\\\end{array}$$

Question 25

Construct a scatter diagram with several groups of uncorrelated data but a strong correlation among all the data.

A)


B)


C)



D)

Question 26

Construct a scatter diagram with two groups of data, correlations within each group, but no correlation among all the data.

A)


B)


C)


D)

Question 27

Select the best-fit line for the data on the scatter diagram. If none of the lines fit the data, write "none of the lines".
Select the best-fit line on the scatter diagram below.

Question 28

The table contains the weights (in pounds)and heights (in inches)of 9 randomly selected adults. Estimate or compute the correlation coefficient. $$\begin{array} { c c } \hline \text { Weight (lb) }&\text {Height (in.) } \\ \hline 150 & 72 \\135 & 68 \\145 & 68 \\145 & 65 \\125 & 60 \\130 & 62 \\128 & 70 \\130 & 65 \\155 & 75 \\\hline\end{array}$$

A)0.54
B)-0.73
C)-0.54
D)0.73

Question 29

To get the best deal on a microwave oven, Amanda called six appliance stores and asked the cost and volume of several models. The prices and volumes she was quoted are listed below. Construct a scatter diagram for the data.


$$\begin{array}{l}\begin{array} { c c } \hline \text { Volume (cu.ft) } & \text { Price (\$) } \\\hline 1.8 & 417 \\1.5 & 463 \\1 & 200 \\1.5 & 17 \\0.7 & 49 \\1.5 & 349 \\1.9 & 183 \\0.5 & 119 \\2.2 & 119 \\\hline\end{array}\\\text { - }\end{array}$$

Question 30

Including the outlier, estimate or compute the correlation coefficient for the complete data set.

A)-0.62
B)-0.83
C)0.83
D)0.62

Question 31

To get the best deal on a microwave oven, Amanda called six appliance stores and asked the cost and volume of several models. The prices and volumes she was quoted are listed below. Estimate or compute the correlation
Coefficient. $$\begin{array} { c c } \hline \text { Volume (cu.ft) } & \text { Price } ( \$ ) \\\hline 0.5 & 119 \\2.2 & 119 \\1.8 & 417 \\1.5 & 463 \\1 & 200 \\1.5 & 17 \\0.7 & 49 \\1.5 & 349 \\1.9 & 183 \\\hline\end{array}$$

A)-0.3
B)0.3
C)-0.7
D)0.7

Question 32

Construct a scatter diagram with two groups of data that have no correlation within either group but shows a moderate correlation among all the data.

A)


B)


C)


D)

Question 33

Select the best-fit line for the data on the scatter diagram. If none of the lines fit the data, write "none of the lines".
Select the best-fit line on the scatter diagram below.

Question 34

Write possible coordinates for the single outlier such that it would no longer be an outlier.

A)(8, 25)
B)(8, 20)
C)(8, 5)
D)(25, 8)

Question 35

Select the best-fit line for the data on the scatter diagram. If none of the lines fit the data, write "none of the lines".
Select the best-fit line on the scatter diagram below.

Question 36

Solve the problem. Round your answers to the nearest whole percent.

-


The scatter diagram shows the data for the prices of a stock (y) and U.S. employment (x). The correlation coeffici $0.8$ . Determine how much of the variation in the stock price can be accounted for by the best-fit line.

A) $80 \%$
B) $36 \%$
C) $20 \%$
D) $64 \%$ cient r is

Question 37

Write possible coordinates for both outliers so that neither would be an outlier.

A)(8, 4)and (16, 19)
B)(8, 0)and (16,0)
C)(8, 19)and (16, 8)
D)(8, 4)and (16, 8)

Question 38

The table contains the weights (in pounds)and heights (in inches)of 9 randomly selected adults. You learn that the five smallest weights were all women. How does this change your view of the correlation? $$\begin{array} { c c } \hline \text { Weight (lb) }& \text {Height (in.) } \\ \hline 128 & 70 \\130 & 65 \\155 & 75 \\150 & 72 \\135 & 68 \\145 & 68 \\145 & 65 \\125 & 60 \\130 & 62\end{array}$$

Question 39

Construct a scatter diagram with several groups of data such that there is no correlation of data within the groups and no correlation among all the data.

A)


B)


C)


D)

Question 40

Select the best-fit line for the data on the scatter diagram. If none of the lines fit the data, write "none of the lines".
Select the best-fit line on the scatter diagram below.

Question 41

Determine whether the stated causal connection is valid or not valid.
The fuel economy of a car is affected by the car's type of upholstery.

A)Valid
B)Not valid

Question 42

Determine whether the stated causal connection is valid or not valid.
Long-distance hikers sometimes get blisters on their feet.

A)Valid
B)Not valid

Question 43

Determine whether the stated causal connection is valid or not valid.
The fuel economy of a car is affected by the car's engine size.

A)Valid
B)Not valid

Question 44

Solve the problem. Round your answers to the nearest whole percent.
The scatter diagram shows the data for attendance at the local team's hockey games (y)and the number of wins (x)for
That team. The correlation coefficient r is 0.4. Determine how much of the variation in attendance can be accounted for
By the best-fit line.

A)16%
B)36%
C)84%
D)25%

Question 45

Solve the problem.

-There is a strong correlation between the number of homicides and the number of gas stations in a town. Local activists claim that building more gas stations will cause the homicide rate to rise. Evaluate the claim of causality.

Question 46

Solve the problem.

-A local highway has an express lane that contains no exits and runs parallel to the other lanes for five miles before merging back with them. A study found that during rush hour traffic, driving times in the express lane were strongly correlated with the longest travel times over the five mile stretch in question. One driver commented that the express lane causes traffic slowdowns and was a waste of money. Comment on how persuasive this comment is and how additional research could help.

Question 47

Answer the question using the value of r and the given best-fit line on the scatter diagram.

- The scatter diagram and best-fit line show the data for the price of a stock (y)and U.S. employment (x). The correlation coefficient r is 0.8. Predict the stock price for an employment value of 5.

A)5.9
B)4.9
C)7
D)No valid prediction is possible.

Question 48

Solve the problem.

-A study found a strong correlation between excessive red meat consumption and cholesterol problems . If excessive red meat consumption causes cholesterol problems , how could some of the people in the study frequently eat red meat and yet show no signs of cholesterol problems ?

Question 49

Solve the problem.

-A reporter studied the causes of household fires in his town and found a strong correlation between the damages (in dollars)and the number of fire trucks at the scene. The reporter's newspaper ran a headline claiming that using more fire trucks at the scene seems to cause more harm than good. Is the newspaper right in
their claim?

Question 50

Answer the question using the value of r and the given best-fit line on the scatter diagram.

- The scatter diagram and best-fit line show the data for the number of cars waiting by a school (y)and the amount of time after the end of classes (x). The correlation coefficient r is -0.55. Predict the number of cars at time 8
After the end of classes.

A)6
B)No valid prediction is possible.
C)5
D)7

Question 51

Answer the question using the value of r and the given best-fit line on the scatter diagram.

- The scatter diagram and best-fit line show the data for price per item (y)and the availability of that item (x). The correlation coefficient r is -0.95. Predict the price per item for an availability of 3.

A)7.8
B)6.8
C)No valid prediction is possible.
D)8.8

Question 52

Determine whether the stated causal connection is valid or not valid.
The distance that a hit golf ball travels is caused by the strength of the golfer.

A)Valid
B)Not valid

Question 53

Solve the problem. Round your answers to the nearest whole percent.
The scatter diagram shows the data for price per item (y)and the availability of that item (x). The correlation coefficient r
Is -0.95. Determine how much of the variation in price per item can be accounted for by the best-fit line.

A)5%
B)10%
C)95%
D)90%

Question 54

Determine whether the stated causal connection is valid or not valid.
Alcohol intoxication can be prevented by drinking light beer.

A)Valid
B)Not valid

Question 55

Answer the question using the value of r and the given best-fit line on the scatter diagram.

-
The scatter diagram and best-fit line show the data for the price of a stock (y)and U.S. employment (x). The correlation coefficient r is 0.8. Predict the stock price for an employment value of 11.

A)9.8
B)9
C)8
D)No valid prediction is possible.