Quiz about AP Stats Ch.3 Review

Question 1

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?

Accepted Answer

There is a moderately weak, positive linear relationship between height and foot length.

Answer

There is some random variation, but otherwise height is directly proportional to foot length.

Answer

There is a roughly linear relationship between height and foot length.

Answer

The relationship between height and foot length is linear, positive, and very strong.

Question 2

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?

Accepted Answer

Children in this city who have a healthy diet in early childhood tend to do better in middle school.

Answer

Ensuring good nutrition in early childhood will increase academic achievement for middle school students.

Answer

Since the correlation is so low, no conclusions can be drawn.

Question 3

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

Accepted Answer

It has the same sign as the correlation coefficient r.

Answer

The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable.

Answer

It is unitless.

Answer

When the x-variable is 0, this is what the y-variable is predicted to be.

Question 4

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

Accepted Answer

The correlation between amount of fertilizer and pounds of tomatoes harvested was found to be r = 0.33.

Answer

The correlation between the gas mileage of a car and its weight is r = -0.71 gallon-pounds.

Answer

The correlation between GPA and hours of sleep per night is r = 1.06.

Answer

There is a correlation of r = 0.54 between the position a football player plays and his or her weight.

Question 5

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?

Accepted Answer

r = 0.9

Answer

r = 0.81

Answer

r = 0.656

Answer

There is no way to know.

Question 6

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?

Accepted Answer

Height = 117.99 + 1.878 (Foot Length)

Answer

Foot Length = 117.99 + 1.878 (Height)

Answer

Height = 1.878 + 117.99 (Foot Length)

Answer

Foot Length = 1.878 + 117.99 (Height)

Question 7

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?

Accepted Answer

LSRL would be different and r would stay the same

Answer

LSRL would be different and r would be different

Answer

LSRL would stay the same and r would be different

Answer

LSRL would stay the same and r would stay the same

Question 8

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

Accepted Answer

The number of people using the shower in a dormitory and the water pressure.

Answer

The hours that an air conditioner runs and the electricity bill at the end of the month.

Answer

The quality of a mattress and the quality of sleep a person gets.

Answer

The price of a home and how big it is.

Question 9

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

Accepted Answer

an outlier and an influential point

Answer

not an outlier or an influential point

Answer

not an outlier but an influential point

Answer

an outlier but not an influential point

Question 10

Forestry managers keep records giving the number of board feet B (in hundreds of board feet) of lumber produced by harvesting white pine trees with diameter D (in inches), so that they can predict the amount of lumber that can be harvested from a tree from its diameter. A scatterplot of B vs. D shows a strongly curved shape, but taking the natural logarithm of both variables produces a linear scatterplot. This computer output below is for a least squares linear regression of vs for 9 white pine trees. Which one of the following is a correct regression equation for these data?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Question 11

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship. Which statement about the slope is true?

Accepted Answer

For each additional 1 mg of caffeine, the study time is predicted to increase by 0.164 hours.

Answer

For each additional 1 hour of study time, the caffeine intake is predicted to increase by 0.164 mg.

Answer

For each additional 1 hour of study time, the caffeine intake is predicted to decrease by 0.164 mg.

Answer

For each additional 1 mg of caffeine, the study time is predicted to decrease by 0.164 hours.

Question 12

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship. Which statement about the y-intercept is true?

Accepted Answer

When the caffeine intake is 0 mg, the study time is predicted to be 2.544 hours.

Answer

When the caffeine intake is 0 mg, the study time is 2.544 hours.

Answer

When the caffeine intake is 0 mg, the study time is predicted to be 0.164 hours.

Answer

When the caffeine intake is 0 mg, the study time is 0.164 hours.

Question 13

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship. How large is a typical prediction error from the actual study time when using this model to predict study time from caffeine intake?

Accepted Answer

1.532 hours

Answer

1.532 milligrams

Answer

60.032%

Answer

2.544 hours

Question 14

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship. About what percentage of the variation in study time can be explained by the regression on caffeine intake?

Accepted Answer

25.4%

Answer

16.4%

Answer

58.6%

Answer

60.0%

AP Stats Ch.3 Review

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