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

Last updated over 1 year 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?

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1

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

Required
2

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.

Required
1

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?

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

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.

Required
3

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.
  1. Construct a segmented bar chart to summarize the relationship between business size and whether or not the business replied to the survey.
  2. 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.
  3. Describe two associations.

Required
4

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.

Required
2

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?

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3

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

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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
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1

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