AP Stats Chapter 3

The following scatterplot describes the relationship between height (in cm) and foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. Which of the following is the best description of this relationship?

• There is some random variation, but otherwise height is directly proportional to foot length.
• There is a roughly linear relationship between height and foot length.
• There is a moderately weak, positive linear relationship between height and foot length.
• The relationship between height and foot length is linear, positive, and very strong.

A sociologist is studying the relationship between early childhood nutrition and academic achievement in middle school among children in a certain city. Which of the following statements about the variable “early childhood nutrition” is correct?

• Early childhood nutrition is a response variable.
• Early childhood nutrition is an explanatory variable.
• Since there is not a clear explanatory-response relationship in this scenario, we cannot classify early childhood nutrition as either explanatory or response.

Which of the following statements about the slope of the least-squares regression line is true? 

• It has the same sign as the correlation coefficient r.
• The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable.
• It is unitless.
• When the x-variable is 0, this is what the y-variable is predicted to be.

One of the following is a correct statement involving correlation. The other three contain blunders. Which one is correct? 

• The correlation between the gas mileage of a car and its weight is r = -0.71 gallon-pounds.
• The correlation between GPA and hours of sleep per night is r = 1.06.
• There is a correlation of r = 0.54 between the position a football player plays and his or her weight.
• The correlation between amount of fertilizer and pounds of tomatoes harvested was found to be r = 0.33.

A study showed that students who spend more time studying for statistics tests tend to achieve better scores on their tests. In fact, the number of hours studied turned out to explain 81% of the observed variation in test scores among the students who participated in the study. What is the value of the correlation between number of hours studied and test score? 

• r = 0.81
• r = 0.656
• r = 0.9
• There is no way to know.

The following computer output describes the relationship between y = height (in cm) and x = foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. The scatterplot for this relationship show a roughly linear shape. Which of the following is an equation of least-squares regression line for these data?

• Height = 117.99 + 1.878 (Foot Length)
• Foot Length = 117.99 + 1.878 (Height)
• Height = 1.878 + 117.99 (Foot Length)
• Foot Length = 1.878 + 117.99 (Height)

The equation of a regression line is y = 0.5x + 35 where x is father’s height in inches and y is son’s height in inches. For a father who is 72 inches tall, what would we predict for the son’s height?

• 69 inches 
• 71 inches 
• 72 inches
• 74 inches

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The point in the upper right hand corner of the scatterplot is

• not an outlier or an influential point
• not an outlier but an influential point
• an outlier and an influential point
• an outlier but not an influential point

With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student’s completion time on a new puzzle was measured. The Residual plot for regression of Completion Time on Practice Time is shown below. Which of the following is correct?

• There is a no relationship between Practice Time and Puzzle Completion Time.

• This regression equation would likely overestimate the Puzzle Completion Time for 175 minutes of practice time.

• There is a non-linear relationship between Practice Time and Puzzle Completion Time.

The dot plot below shows the annual salaries, in thousands of dollars, of a sample of non-management staff who work for a small banking company.

Which of the following statistics would be the most reasonable estimate of the typical annual salary?

• Mean

• Mode

• Median

• Interquartile range