Question 1

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-For each of the three variables displayed in the plot, state whether they are categorical or quantitative.
Weight:
Gestation:
Smoke:

Accepted Answer

Weight: quantitative
Gestation: quantitative
Smoke: categorical

Question 2

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-Based on the plot, does there appear to be an association between gestation period and birth weight?
A) Yes, because as one variable increases, the other tends to increase as well.
B) No, because as one variable increases, the other tends to increase as well.
C) Yes, because most of the circles on the plot appear to be higher than the triangles.
D) No, because one variable does not appear to change the other variable.

Accepted Answer

There is an association because as the gestation period increases, the birth weight tends to increase as well, indicating a positive correlation.

Question 3

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-Is whether the mother smoked during pregnancy a confounding variable in describing the relationship between gestation period and birth weight?
A) No, because smoking status is not associated with gestation period.
B) No, because smoking status is not associated with birth weight.
C) Yes, because mothers who smoke tend to have lighter babies, and mothers who smoke also tend to have shorter gestation periods.
D) Yes, because mothers who smoke tend to have heavier babies, and mothers who smoke also tend to have longer gestation periods.
E) We cannot determine whether smoking status is a confounding variable based on this plot.

Accepted Answer

Smoking during pregnancy is a confounding variable because it is associated with both a shorter gestation period and lower birth weight, potentially influencing the observed relationship between these two variables.

Question 4

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-Does the association between gestation period and birthweight appear to depend on smoking status?
A) Yes, since the regression line for non-smokers is higher than the regression line for smokers.
B) Yes, since the regression line for non-smokers would have a higher y-intercept than the regression line for smokers.
C) No, since the regression line for non-smokers and the regression line for smokers have similar slopes.
D) No, since the sample sizes of smokers and non-smokers are similar.

Accepted Answer

The answer of Babies born with low birth weights (less...

Question 5

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-How would the correlation coefficient between birth weight and gestation period computed from all women in the sample compare to the correlation coefficient between birth weight and gestation period computed from only non-smoking women?
A) The correlation coefficient for the entire sample would be closer to 1 than the correlation coefficient for the non-smoking group.
B) The correlation coefficient for the entire sample would be closer to 0 than the correlation coefficient for the non-smoking group.
C) The correlation coefficient for the entire sample would be the same as the correlation coefficient for the non-smoking group.
D) We cannot determine how the two correlation coefficients compare based on this plot.

Accepted Answer

Smoking is a confounding variable that can affect birth weight, potentially weakening the correlation in the entire sample compared to the non-smoking group.

Question 6

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. 
-What type of plot would be appropriate for examining the relationship between a mother's age and her baby's birth weight?
A) Scatterplot
B) Side-by-side boxplots
C) Segmented bar graph
D) Dotplot

Accepted Answer

A scatterplot is appropriate for examining the relationship between two continuous variables, such as a mother's age and her baby's birth weight.

Question 7

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). 
-What is the form of this scatterplot?
A) Linear
B) Non-linear

Accepted Answer

The answer of The following scatterplot displays the finish time...

Question 8

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). 
-What is the direction of the association between finish time and age?
A) Positive
B) Negative

Accepted Answer

As age increases, finish time typically increases, indicating a positive association.

Question 9

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). 
-Approximate the value of the correlation coefficient for these data.
A) 0
B) 0.25
C) 0.50
D) 0.80

Accepted Answer

The answer of The following scatterplot displays the finish time...

Question 10

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). 
-If 70-year-old male with a finishing time of 35 minutes was added to the data set, would the correlation coefficient increase, decrease, or remain the same?
A) Increase
B) Decrease
C) Remain the same
D) Unable to determine with the information provided

Accepted Answer

Adding a 70-year-old male with a finishing time of 35 minutes would likely be an outlier, potentially weakening the existing correlation and causing the correlation coefficient to decrease.

Question 11

Which of the following plots has the strongest correlation between the two variables plotted?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following plots has the...

Question 12

Estimate the value of the correlation coefficient between the two variables shown in the following scatterplot. 
A) 0.90
B) 0.80
C) -0.80
D) 0.09

Accepted Answer

The answer of Estimate the value of the correlation coefficient...

Question 13

If the correlation coefficient between variables x and y is equal to zero, then we can say that x and y are not associated.

Accepted Answer

A correlation coefficient of zero indicates no linear relationship, but there may still be a non-linear association between x and y.

Question 14

The graph below shows a scatter plot of medical expenses in the past year by age for a sample of Americans.  Which one of the following is a true statement about the data shown in the graph?
A) The correlation must be close to one because there is a strong relationship between age and medical expenses.
B) Using correlation on the data shown in the graph above is not appropriate because the relationship shown in the graph is not linear.
C) Both A and B are true statements.
D) Neither A nor B is a true statement.

Accepted Answer

The answer of The graph below shows a scatter plot...

Question 15

Which of the following correlation coefficient values describes the weakest linear association between two variables.
A) -0.99
B) -0.23
C) 0.12
D) 0.38

Accepted Answer

A correlation coefficient close to 0 indicates a weak linear association. 0.12 is closest to 0 among the given options.

Question 16

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. 
-Approximate the value of the correlation coefficient for these data.
A) 0.10
B) 0.40
C) 0.80
D) 0

Accepted Answer

The answer of Are people with bigger brains more intelligent?...

Question 17

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. 
-State the null and alternative hypotheses using proper notation.
A)  versus 
B)  versus 
C)  versus 
D)  versus

Accepted Answer

The answer of Are people with bigger brains more intelligent?...

Question 18

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. 
-Select the best explanation for how one sample would be simulated in order to generate the null distribution.
A) Flip a coin to decide whether to swap the values for brain size and IQ or not. Plot the correlation coefficient of the randomized points on the null distribution.
B) Holding the order of brain size values constant, randomize the order of the IQs. Plot the correlation coefficient of the shuffled data on the null distribution.
C) Put each pair of (brain size, IQ) on a piece of paper. Draw with replacement 40 times. Plot the correlation coefficient of the resampled data on the null distribution.
D) Add or subtract the appropriate value from each brain size and IQ in order to force the null hypothesis to be true. Plot the correlation coefficient of the shifted data on the null distribution.

Accepted Answer

Randomizing the order of IQs while keeping brain size constant simulates the null hypothesis of no relationship, allowing for the generation of a null distribution of correlation coefficients.

Question 19

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. 
-Below is a picture of a simulated null distribution of correlation coefficients created using the Corr/Regression applet. How would you use this distribution to calculate the p-value? 
A) Find the proportion of simulated correlation coefficients greater than zero.
B) Find the proportion of simulated correlation coefficients as far away from zero or further than the one observed.
C) Find the proportion of simulated correlation coefficients as small or smaller than the one observed.
D) Find the proportion of simulated correlation coefficients as large or larger than the one observed.

Accepted Answer

The answer of Are people with bigger brains more intelligent?...

Question 20

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. 
-The p-value for this test is 0.008. What can we conclude?
A) We have strong evidence that an increase in brain size will increase IQ.
B) We have strong evidence that an increase in brain size is associated with an increase in IQ.
C) We have strong evidence that an increase in IQ will increase brain size.
D) We have strong evidence that brain size and IQ are not associated.

Accepted Answer

The p-value is less than 0.05, which means that there is a statistically significant association between brain size and IQ. The direction of the association is positive, meaning that an increase in brain size is associated with an increase in IQ.

Quiz 11: Two Quantitative Variables

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande) . -What is the form of this scatterplot?

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande) . -What is the direction of the association between finish time and age?

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande) . -Approximate the value of the correlation coefficient for these data.

Which of the following plots has the strongest correlation between the two variables plotted?

Estimate the value of the correlation coefficient between the two variables shown in the following scatterplot.

If the correlation coefficient between variables x and y is equal to zero, then we can say that x and y are not associated.

The graph below shows a scatter plot of medical expenses in the past year by age for a sample of Americans. Which one of the following is a true statement about the data shown in the graph?

Which of the following correlation coefficient values describes the weakest linear association between two variables.