Copy of Practice Ch. 2 Test (10/5/2023)

Last updated almost 2 years ago

18 questions

Required

1

Required

1

Required

1

Required

1

Required

1

Required

1

Required

2

Required

1

Required

1

Required

1

Required

3

Required

4

Required

2

Required

3

Required

1

Required

1

Required

1

Required

1

Library

Copy of Practice Ch. 2 Test (10/5/2023)

Last updated almost 2 years ago

18 questions

Required

1

Biologists assess how closely related similar species are by measuring the number of years since the two species diverged from a common ancestor.
Researchers compared the years since divergence for 12 different pairs of sunfish species to the hatching success of eggs produced by a “cross” between the two species.
A scatterplot of their results is shown. A hatching success of 100 means the hybrid eggs hatched as often as single-species eggs hatched. A number below 100 means the hybrid eggs hatch less often.

Which of the following is closest to the correlation between these two variables?

Required

1

Which of the following statements is true of the correlation r between the length in inches and weight in pounds of a sample of brook trout?

Required

1

The scatterplot shows the relationship between life expectancy (in years) and Internet users (per 100 individuals in the population) for 35 countries in North and South America, along with the least-squares regression line.

Haiti had 8.37 Internet users per 100 people and a life expectancy of 45 years.
What effect would removing this outlier point for Haiti have on the regression line?

Required

1

In a certain population there is an approximately linear relationship between
y = height of females (in centimeters) and
x = their age (in years, from 5 to 18)
Described by the equation: y-hat = 50.3 + 6.1x
Which one of the following statements must be true?
Think about how we have interpreted slope and the y-intercept in class.

Required

1

Scientists examined the activity level of 7 fish at different temperatures. The least-squares regression equation was calculated for the relationship between y = fish activity (rated as 0 = no activity and 100 = maximal activity) and x = water temperature in degrees Celsius.
The regression calculation produced a value of s = 4.785.
Which of the following gives a correct interpretation of s in this setting?

Required

1

The fraction of the variation in the values of y that is accounted for by the least-squares regression equation is...

Required

2

Required

1

Required

1

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average.
The guidance counselor says, “The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero.”
A correct interpretation of this statement would be that

Required

1

Required

3

Required

4

Required

2

Required

3

Required

1

Sarah’s parents are concerned that she seems short for her age. Their doctor has the following record of Sarah’s height:
Age (months): 36, 48, 51, 54, 57, 60
Height (cm): 86, 90, 91, 93, 94, 95

Copy and paste the data into statsmedic.com/applets (2 quantitative variables) to create a scatterplot.
What is the linear regression equation?
Make sure to use the variables listed above instead of x and y for full credit.
Use -hat to indicate which variable is being predicted.

Required

1

Use your equation from #14 to calculate the residual for Sarah's height when she was 48 months.
Remember, you first need to calculate the predicted height:_______ keep all decimal places
Then calculate the residual:_______ keep all decimal places
What does this tell us about the regression model for predicting height based on age? Did it over or under predict? _______ 

Required

1

Using the regression model from #14, predict Sarah’s height at age 40 years (480 months). 
Height at 40 years = _______ keep all decimals
Convert your prediction to inches (2.54 centimeters = 1 inch). _______ 
Now convert to feet (12 inches = 1 foot). _______ round to one place past the decimal

Required

1

The prediction is impossibly large. Explain why this happened and what this type of prediction is called.

Biologists assess how closely related similar species are by measuring the number of years since the two species diverged from a common ancestor.
Researchers compared the years since divergence for 12 different pairs of sunfish species to the hatching success of eggs produced by a “cross” between the two species.
A scatterplot of their results is shown. A hatching success of 100 means the hybrid eggs hatched as often as single-species eggs hatched. A number below 100 means the hybrid eggs hatch less often.

Which of the following is closest to the correlation between these two variables?

Which of the following statements is true of the correlation r between the length in inches and weight in pounds of a sample of brook trout?

The scatterplot shows the relationship between life expectancy (in years) and Internet users (per 100 individuals in the population) for 35 countries in North and South America, along with the least-squares regression line.

Haiti had 8.37 Internet users per 100 people and a life expectancy of 45 years.
What effect would removing this outlier point for Haiti have on the regression line?

In a certain population there is an approximately linear relationship between
y = height of females (in centimeters) and
x = their age (in years, from 5 to 18)
Described by the equation: y-hat = 50.3 + 6.1x
Which one of the following statements must be true?
Think about how we have interpreted slope and the y-intercept in class.

Scientists examined the activity level of 7 fish at different temperatures. The least-squares regression equation was calculated for the relationship between y = fish activity (rated as 0 = no activity and 100 = maximal activity) and x = water temperature in degrees Celsius.
The regression calculation produced a value of s = 4.785.
Which of the following gives a correct interpretation of s in this setting?

The fraction of the variation in the values of y that is accounted for by the least-squares regression equation is...

There is a strong positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital.
Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?
Select both correct answers.

Derek Jeter, the New York Yankees’ star shortstop, retired after the 2014 season.
A linear regression model and quadratic regression model were calculated to predict:
y = the number of home runs Jeter hit in a given year from x = his age that year.
Here are the residual plots for each model.

Which of the following statements is supported by these residual plots?

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average.
The guidance counselor says, “The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero.”
A correct interpretation of this statement would be that

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large.
Questionnaires were sent to 200 randomly selected businesses of each size.
Because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business.
The data are given in the two-way table.
Which variable should be used as the explanatory variable? Explain.

Use the table from #10, go to statsmedic.com/applets.
Are you using 2 categorical variables or 2 quantitative variables? This will determine which applet you use.
Construct a segmented bar chart to summarize the relationship between business size and whether or not the business replied to the survey.
Use your graph from part 1 to determine if there is an association between the size of business and whether or not the business replied to the survey.
Describe two associations.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.
Describe the association shown in the scatterplot. Use D.O.F.S. to find four answers.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.
The correlation coefficient, r = 0.59.
What does the correlation coefficient tell us about the relationship between height and field goal percentage?

Use the following regression equation for the relationship between height and field goal percentage:
Which variable is being predicted by which variable?

Sarah’s parents are concerned that she seems short for her age. Their doctor has the following record of Sarah’s height:
Age (months): 36, 48, 51, 54, 57, 60
Height (cm): 86, 90, 91, 93, 94, 95

Copy and paste the data into statsmedic.com/applets (2 quantitative variables) to create a scatterplot.
What is the linear regression equation?
Make sure to use the variables listed above instead of x and y for full credit.
Use -hat to indicate which variable is being predicted.

Use your equation from #14 to calculate the residual for Sarah's height when she was 48 months.
Remember, you first need to calculate the predicted height:_______ keep all decimal places
Then calculate the residual:_______ keep all decimal places
What does this tell us about the regression model for predicting height based on age? Did it over or under predict? _______ 

Using the regression model from #14, predict Sarah’s height at age 40 years (480 months). 
Height at 40 years = _______ keep all decimals
Convert your prediction to inches (2.54 centimeters = 1 inch). _______ 
Now convert to feet (12 inches = 1 foot). _______ round to one place past the decimal

The prediction is impossibly large. Explain why this happened and what this type of prediction is called.

0.2

-0.2

r = 1.25 shows a strong correlation.

Slope would increase; y intercept would decrease.

Slope would decrease; y intercept would decrease.

The estimated intercept is 50.3 centimeters. We know from the intercept that the typical height of girls in this population at birth is 50.3 centimeters.

A 10-year-old girl in this population is at least 110.3 centimeters tall.

The typical distance of the activity level ratings from the least-squares line is about 4.785 units.

For every 1°C increase in temperature, fish activity is predicted to increase by 4.785 units.

There is a strong positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital. 
Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?
Select both correct answers.

Yes; but only if r is very close to 1.

No; a negative correlation would allow that conclusion, but this correlation is positive.

No; the positive correlation probably arises because seriously ill people go to large hospitals.

Correlation between # of beds and number of days at a hospital does not mean # of beds causes more days at the hospital.

Correlation between # of beds and number of days at a hospital shows an increase in # of beds causes more days at the hospital.

Yes; the positive correlation establishes that a larger hospital size is the reason for longer stays.

Derek Jeter, the New York Yankees’ star shortstop, retired after the 2014 season. 
A linear regression model and quadratic regression model were calculated to predict:
 y = the number of home runs Jeter hit in a given year from x = his age that year. 
Here are the residual plots for each model. 

Which of the following statements is supported by these residual plots?

The quadratic model is a better fit because there is a U- shaped pattern in the residuals of the quadratic model.

The linear model is a better fit because there is an upside-down, U-shaped pattern in the residuals of the linear model.

students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities.

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. 
Questionnaires were sent to 200 randomly selected businesses of each size. 
Because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business. 
The data are given in the two-way table.
Which variable should be used as the explanatory variable? Explain.

If there was a response would more likely be used to predict the business size.

There is no association, business size is not related to if the employees respond to a survey.

Use the table from #10, go to statsmedic.com/applets.
Are you using 2 categorical variables or 2 quantitative variables? This will determine which applet you use.
Construct a segmented bar chart to summarize the relationship between business size and whether or not the business replied to the survey.
Use your graph from part 1 to determine if there is an association between the size of business and whether or not the business replied to the survey.
Describe two associations.

Large businesses are more likely to respond to the survey.

Small businesses are least likely to respond to the survey.

Large businesses are least likely to respond to the survey.

Medium businesses are more likely to respond to the survey.

No, there is not an association between business size and whether or not the business replied to the survey.

Yes, there is an association between business size and whether or not the business replied to the survey.

Medium businesses are least likely to respond to the survey.

Small businesses are more likely to respond to the survey.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.
Describe the association shown in the scatterplot. Use D.O.F.S. to find four answers.

The direction is positive.

The direction is negative.

There is no direction.

The form linear.

The form is nonlinear.

There is a possible outlier.

There are no outliers.

The association appears to be strong.

The association appears to be weak.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.
The correlation coefficient, r = 0.59.
What does the correlation coefficient tell us about the relationship between height and field goal percentage?

There is no direction.

The association is moderate.

The association is strong.

The direction is negative.

The form linear.

The direction is positive.

The association is weak.

The form is nonlinear.

Use the following regression equation for the relationship between height and field goal percentage:
 Which variable is being predicted by which variable?

The 'hat' notation tells us the variable that is being predicted.

We can also see the predictor variable on the x axis.

The 'hat' notation tells us the variable that is doing the predicting.

Height is being predicted by field goal %.

We can also see the predictor variable on the y axis.

Field goal % is being predicted by height.

Copy of Practice Ch. 2 Test (10/5/2023)

Copy of Practice Ch. 2 Test (10/5/2023)

Which of the following statements is true of the correlation r between the length in inches and weight in pounds of a sample of brook trout?

The fraction of the variation in the values of y that is accounted for by the least-squares regression equation is...

The prediction is impossibly large. Explain why this happened and what this type of prediction is called.

Which of the following statements is true of the correlation r between the length in inches and weight in pounds of a sample of brook trout?

The fraction of the variation in the values of y that is accounted for by the least-squares regression equation is...

There is a strong positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?Select both correct answers.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.Describe the association shown in the scatterplot. Use D.O.F.S. to find four answers.

Use the following regression equation for the relationship between height and field goal percentage: Which variable is being predicted by which variable?

The prediction is impossibly large. Explain why this happened and what this type of prediction is called.

There is a strong positive correlation between the size of a hospital (measured by number of beds) and the median number of days that patients remain in the hospital.
Does this mean that you can shorten a hospital stay by choosing to go to a small hospital?
Select both correct answers.

The scatterplot displays the relationship between height and field-goal percentage for all the basketball players on the 2013 roster of the Brooklyn Nets.
Describe the association shown in the scatterplot. Use D.O.F.S. to find four answers.

Use the following regression equation for the relationship between height and field goal percentage:
Which variable is being predicted by which variable?