Question 1

An introductory statistics class decides to investigate whether there is a relationship between the performance on midterms 1 and 2. The instructor creates a scatterplot of midterm 2 scores (y) versus midterm 1 scores (x).  Based on the plot, which of the following is likely true?
A)The correlation between midterm 1 and midterm 2 scores is positive.
B)Students who did well on midterm 1 did not do so well on midterm 2, and vice versa.
C)There is no relationship between midterm 1 and midterm 2 performance.
D)None of the answer options is correct.

Accepted Answer

The scatterplot shows a positive linear relationship between midterm 1 and midterm 2 scores, indicating that as midterm 1 scores increase, so do midterm 2 scores. Therefore, choice A is likely true. Choice B can be ruled out because the scatterplot does not show a negative relationship between the two variables. Choice C can also be ruled out because there is a clear pattern shown in the scatterplot, indicating a relationship.

Question 2

What can be said of the correlation between the brand of an automobile and its quality?
A)The correlation is negative, because smaller cars tend to have higher quality and larger cars tend to have lower quality.
B)The correlation is positive, because better brands have higher quality.
C)If the correlation is negative, an arithmetic mistake was made; correlation must be positive.
D)Correlation makes no sense here, because brand is a categorical variable.

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two quantitative variables. Since "brand" is a categorical variable and "quality" can be considered quantitative, calculating a correlation coefficient between these two does not make sense. Correlation requires both variables to be quantitative.

Question 3

A researcher states that bone density in women is negatively associated with age. This means that:
A)as women get older, bone density tends to decrease.
B)as women get older, bone density tends to increase.
C)below-average values of age tend to accompany below-average values of bone density.
D)older women aren't any more likely than younger women to have below-average bone density.

Accepted Answer

The term "negative association" implies an inverse relationship between two variables. In this case, as age increases, bone density tends to decrease, which corresponds to option A.

Question 4

Archaeologists often find only parts of ancient human remains. For example, they may find a small finger bone, called the metacarpal bone. Is it possible to predict the height of a human from the length of a metacarpal bone? To investigate, a researcher measures the heights and metacarpal lengths of 200 adults. In making the scatterplot, the researcher should:
A)plot the height of the person on the horizontal axis.
B)plot the metacarpal length on the horizontal axis.
C)first determine if the heights of humans follow a Normal distribution.
D)use a plotting scale that makes the overall trend roughly linear.

Accepted Answer

In order to investigate the relationship between metacarpal length and height, it is important to plot metacarpal length on the horizontal axis. This allows us to visualize how the length of the bone relates to the height of the person. Additionally, it is not necessary to determine if the heights follow a Normal distribution for this type of analysis. Lastly, using a linear scale for the plot is important to accurately show the overall trend between the variables.

Question 5

Are higher than average sea surface temperatures associated with a greater than average number of hurricanes each year? In a 2010 study, the average global sea surface temperature anomaly was recorded, along with the number of Atlantic hurricanes above or below the average for that year. The response variable is:
A)the number of hurricanes above or below average.
B)the global sea surface temperature anomaly.
C)the number of hurricanes used in the study.
D)None of the answer options is correct.

Accepted Answer

The response variable in this study is the number of hurricanes above or below average, and the study is examining the relationship between this variable and the sea surface temperature anomaly. Therefore, option A is the correct choice. The other options are incorrect, as they do not accurately describe the response variable or the purpose of the study.

Question 6

A group of students participated in an experiment to study the association between resting heart rate and exercise heart rate under various exercise conditions. Study participants stepped at a frequency of 14 steps per minute (0), 21 steps per minute (1), and 28 steps per minute (2). To investigate the relationship between resting and exercise heart rate, and to see the effects of step frequency on the relationship, a scatterplot might be created by:
A)plotting resting heart rate on the y axis and exercise heart rate on the x axis.
B)plotting exercise heart rate on the y axis and step frequency on the x axis.
C)using separate symbols for the different step frequencies to see if the relationship is affected by step frequency, while plotting resting heart rate on the x axis and exercise heart rate on the y axis.
D)None of the answer options is correct.

Accepted Answer

To investigate the relationship between resting and exercise heart rate, and to examine the effects of step frequency, plotting resting heart rate on the x-axis and exercise heart rate on the y-axis with separate symbols for different step frequencies allows for analysis of both the primary relationship and the influence of step frequency.

Question 7

The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 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.  The scatterplot suggests that there is:
A)a positive association between the volume of oxygen consumed at rest and while running.
B)an outlier in the plot.
C)both a positive association between volume of oxygen consumed at rest and while running, and an outlier in the plot.
D)neither a positive association between volume of oxygen consumed at rest and while running, nor an outlier in the plot.

Accepted Answer

The answer of The volume of oxygen consumed (in liters...

Question 8

Below is a scatterplot of the number of home runs versus the number of stolen bases for major league teams in 2009. American League teams are represented by filled circles, and National League teams are represented by open circles.  We conclude that:
A)there is a strong positive association for American League teams but a negative association for National League teams.
B)there is a strong negative association for American League teams but a positive association for National League teams.
C)there is no association for either league.
D)all American League teams hit more home runs and stole more bases than did National League teams.

Accepted Answer

There does not appear to be a strong association for either league, as there are data points scattered throughout the plot for both leagues. Additionally, the question does not provide any information to support choice D.

Question 9

Colleges often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the studies described:
A)annual income is an explanatory variable.
B)the correlation between annual income and the size of the donation is positive.
C)the size of the donation to the annual fund is the response variable.
D)All of the answer options are correct.

Accepted Answer

All of the answer options are correct. The studies suggest that annual income is an explanatory variable and that there is a reasonably strong, positive, linear relationship between annual income and the size of the donation. Therefore, the size of the donation to the annual fund is the response variable.

Question 10

When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table:  The association between flow rate and the amount of eroded soil is:
A)positive.
B)negative.
C)neither positive nor negative.
D)impossible to determine, because both variables are categorical.

Accepted Answer

As the flow rate increases, the amount of eroded soil also increases. This positive relationship indicates that there is a direct association between the two variables.

Question 11

The graph below shows a scatterplot of midterm scores plotted against homework scores. The graph contains several points that correspond to unusually low homework scores, and one of those scores is associated with the highest midterm score.  Removing this point will:
A)increase the correlation.
B)leave the correlation unchanged.
C)decrease the correlation.
D)The effect cannot be determined from the scatterplot.

Accepted Answer

The answer of The graph below shows a scatterplot of...

Question 12

A student wonders if people with similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the pairs of data (heights in inches):  Which of the following statements is true?
A)The variables measured are all categorical.
B)There is a strong positive correlation between the heights of men and women, because the women are always smaller than the men they date.
C)There is a positive correlation between the heights of men and women.
D)Correlation makes no sense here, because gender is a categorical variable.

Accepted Answer

The data involves measuring heights, which are quantitative variables. The question is exploring whether there is a relationship between the heights of men and women, which can be explored through correlation. While gender is a categorical variable, it is not being used as the variable of interest in this case - heights are. The fact that the women are smaller than the men they date doesn't necessarily mean there is a strong positive correlation, as there could be outliers or other factors at play. Therefore, the statement that there is a positive correlation between the heights of men and women is the best choice.

Question 13

The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 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 at rest.
B)the volume of oxygen consumed while running.
C)the instrument used to measure the volume of oxygen consumed.
D)either variable-it doesn't matter which is considered the response.

Accepted Answer

The explanatory variable is the one that is thought to have an effect on the response variable. In this case, the researchers are trying to determine if the volume of oxygen consumed during exercise can be estimated from the amount consumed at rest. Therefore, the amount of oxygen consumed at rest is the explanatory variable, and the amount consumed during exercise is the response variable.

Question 14

Which of the following statements is correct?
A)Changing the units of measurement of x or y does not change the value of the correlation r.
B)A negative value for the correlation r indicates the data are strongly unassociated.
C)The correlation always has the same units as the x variable but not the y variable.
D)The correlation always has the same units as the y variable but not the x variable.

Accepted Answer

Changing the units of measurement of x or y does not change the value of the correlation coefficient r. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables and is unitless. Therefore, changing the units of measurement of x or y does not affect its value. Option B is wrong because a negative correlation coefficient implies that the two variables are related, but in an inverse or opposite manner. The values of one variable increases while the other decreases. Option C and D are incorrect because the correlation coefficient is a unitless measure of association.

Question 15

For each menu item at a fast food restaurant, the fat content (in grams) and the number of calories were recorded. A scatterplot of these data is given:  A plausible value for the correlation between fat content and number of calories is:
A)+0.2.
B)-0.9.
C)+0.9.
D)-1.0.

Accepted Answer

Based on the scatterplot, there appears to be a strong positive linear relationship between fat content and number of calories, with a tight cluster of points extending from the bottom left to the top right of the graph. Therefore, a plausible value for the correlation between these variables is +0.9, indicating a strong, positive relationship. Option A is unlikely as the points do not seem to deviate in a random fashion. Option B and D are unlikely as there is clearly a linear relationship between the variables, and correlation lies between -1 and +1.

Question 16

A scatterplot can be used to illustrate the relationship between:
A)two categorical variables.
B)one categorical variable and one quantitative variable.
C)two quantitative variables.
D)All of the answer options are correct.

Accepted Answer

A scatterplot is specifically designed to show the relationship between two quantitative variables. This can be useful in identifying patterns or trends in the data, and determining if a relationship exists between the two variables. While scatterplots can be used with categorical variables, they are more appropriate for quantitative data.

Question 17

A scatterplot of the amount of alcohol consumed according to a food diary (DR) against the amount of alcohol consumed on a frequent food questionnaire (FFQ):
A)shows the relationship between the answers from the DR and the FFQ.
B)assesses whether the relationship between the answers on the DR and the FFQ is positive.
C)shows the answers each study participant gave on the FFQ and the DR.
D)All of the answer options are correct.

Accepted Answer

A scatterplot visually represents the relationship between two variables, in this case, the amount of alcohol consumed as reported in a food diary (DR) and a frequent food questionnaire (FFQ). It can show the overall pattern of the relationship (whether it's positive, negative, or non-linear) and display the individual data points for each participant, indicating their reported alcohol consumption on both the DR and FFQ.

Question 18

The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 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.  If the outlier is removed, the correlation coefficient r will:
A)increase.
B)decrease.
C)neither increase nor decrease.
D)There is not enough information to determine the effect on r.

Accepted Answer

The outlier has a strong influence on the correlation coefficient as it significantly deviates from the pattern of the other points. Removing the outlier will result in a higher correlation coefficient.

Question 19

A researcher measures the correlation between two variables. This correlation tells us:
A)whether there is a relation between two variables.
B)whether a scatterplot shows an interesting pattern.
C)whether a cause-and-effect relation exists between two variables.
D)the strength and direction of a linear association between two variables.

Accepted Answer

Correlation tells us the strength and direction of a linear association between two variables, but it does not establish a cause-and-effect relationship between them. It does indicate whether there is a relation between two variables, but it is not related to whether a scatterplot shows an interesting pattern. Hence, option D is the correct choice.

Question 20

Does exposure to classical music (through instrument lessons or concert attendance) improve a child's scholastic performance? In a study, researchers measured the amount of exposure to classical music for a group of children, along with their scores on the state's academic proficiency exam. The explanatory variable in this study is:
A)the type of instrument a child plays.
B)the child's score on the state's proficiency exam.
C)the amount of exposure a child has to classical music.
D)whether a child passed the state's proficiency exam.

Accepted Answer

The explanatory variable in this study is the amount of exposure a child has to classical music. This is the variable that is being studied to see if it has an impact on a child's scholastic performance. The other answer choices are either irrelevant or part of the outcome variable.

Quiz 5: Scatterplots and Correlation

An introductory statistics class decides to investigate whether there is a relationship between the performance on midterms 1 and 2. The instructor creates a scatterplot of midterm 2 scores (y) versus midterm 1 scores (x) . Based on the plot, which of the following is likely true?

What can be said of the correlation between the brand of an automobile and its quality?

A researcher states that bone density in women is negatively associated with age. This means that:

Below is a scatterplot of the number of home runs versus the number of stolen bases for major league teams in 2009. American League teams are represented by filled circles, and National League teams are represented by open circles. We conclude that:

The graph below shows a scatterplot of midterm scores plotted against homework scores. The graph contains several points that correspond to unusually low homework scores, and one of those scores is associated with the highest midterm score. Removing this point will:

A student wonders if people with similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the pairs of data (heights in inches) : Which of the following statements is true?

Which of the following statements is correct?

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

A scatterplot can be used to illustrate the relationship between:

A scatterplot of the amount of alcohol consumed according to a food diary (DR) against the amount of alcohol consumed on a frequent food questionnaire (FFQ) :

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