AP Stats Ch.3 Review

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.

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CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

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.

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CCSS.HSS.ID.C.9

A sociologist studying the relationship between early childhood nutrition and academic achievement in middle school among children in a certain city finds that the correlation between these two variables is 0.86. Which of the following conclusions can he draw from this study?

• Ensuring good nutrition in early childhood will increase academic achievement for middle school students.
• Children in this city who have a healthy diet in early childhood tend to do better in middle school.
• Since the correlation is so low, no conclusions can be drawn.

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CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9

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.

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CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

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.

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CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9

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.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9

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)

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CCSS.HSA.CED.A.2

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

 If you graphed height as the explanatory variable and weight as the response variable, what would happen to the LSRL and r if you had accidently graphed the weight as the explanatory variable and the height as the response variable?

• LSRL would be different and r would be different
• LSRL would be different and r would stay the same
• LSRL would stay the same and r would be different
• LSRL would stay the same and r would stay the same

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CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9

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

Tags

CCSS.8.EE.C.8C

Which of the following relationships is most likely to result in a strong negative relationship?

• The hours that an air conditioner runs and the electricity bill at the end of the month.         
• The number of people using the shower in a dormitory and the water pressure.
• The quality of a mattress and the quality of sleep a person gets.
• The price of a home and how big it is.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9