AP Statistics Unit 2 Multiple Choice

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was y=10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

a. 85.5

b. 90

c. 95

d. 95.5

e. None of the above

d. 95.5

Refer to the previous problem. On the final exam Carla scored 98. What is the value of her residual?

a. -2.5

b. 0

c. 2.5

d. 98

e. None of the above

c. 2.5

All but one of the following statements contains a blunder. Which statement could be correct?

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

b. We found a correlation of r= -0.63 between gender and political party preference.

c. The correlation between the gas mileage of a car and its weight is r=0.71 mpg.

d. We found a high correlation (r=1.09) between height and age of children.

e. The correlation between planting rate and yield of tomatoes was found to be r=0.23.

e. The correlation between planting rate and yield of tomatoes was found to be r=0.23.

You have data for many families on the parents' income and the years of education their eldest child completes. When you make your scatterplot,

a. the explanatory variable is parents' income, and you expect to see a negative association.

b. the explanatory variable is parents' income, and you expect to see a positive association.

c. the explanatory variable is parents' income, and you expect to see very little association.

d. the explanatory variable is years of education, and you expect to see a negative association.

e. the explanatory variable is years of education, and you expect to see a positive association.

b. the explanatory variable is the parents' income, and you expect to see a positive association.

There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by height = 50.3+6.01 (age) where height is measured in centimeters and age in years. Which of the following is not correct?

a. The estimated slope is 6.01, which implies that children increase by about 6 cm for each year they grow older.

b. The estimated height of a child who is 10 years old is about 110 cm.

c. The estimated intercept is 50.3 cm, which implies that children reach this height when they are 50.3/6.01=8.4 years old.

d. The average height of children when they are 5 years old is about 50% of the average height when they are 18 years old.

e. My niece is about 8 years old and is about 115 cm tall. She is taller than average.

c. The estimated intercept is 50.3 cm, which implies that children reach this height when they are 50.3/6.01=8.4 years old.

In the scatterplot in the previous question, if each x-value were decreased by one unit and the y-values remained the same, then the correlation r would...

a. decrease by one unit

b. decrease slightly

c. increase slightly

d. stay the same

e. can't tell without knowing the data values.

d. stay the same.

A regression of the amount of calories in a serving of breakfast cereal vs the amount of fat gave the following results: Calories = 97.1053+9.6525 (Fat). Which of the following is FALSE?

a. It is estimated that for every additional gram of fat in the cereal, the number of calories increases by about 10.

b. It is estimated that in cereals with no fat, the total amount of calories is about 97.

c. If a cereal has 2 g of fat, then it is estimated that the total number of calories is about 116.

d. The correlation between amount of fat and calories is positive.

e. One cereal has 140 calories and 5 g of fat. Its residual is about 5 cal.

e. One cereal has about 140 calories and 5 g of fat. Its residual is about 5 cal.

Which of the following statements is/are true?

I. Correlation and regression require explanatory and response variables.

II. Scatterplots require that both variables be quantitative.

III. Every least-squares regression line passes through (X bar, Y bar).

a. I and II only

b. I and III only

c. II and III only

d. I, II, and III

e. None of the above

c. II and III only

A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the college that

a. the entrance exam is a good predictor of success.

b. the exam is a poor predictor of success.

c. students who do best on this exam will be poor students.

d. students at this school are underachieving.

e. the college should hire a new statistician.

e. the college should hire a new statistician.

A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations given are X bar=8.4, Sx=2.1, Y bar=14.2, Sy=3.8, and r=0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers?

a. 0.86

b. 1.56

c. 0.48

d. None of these

e. Can't tell from the information given

b. 1.56

In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?

a. 86%

b. 93%

c. 74%

d. None of these

e. Can't tell from the information given

c. 74%

If data set A of (x, y) data has correlation coefficient r=0.65, and a second data set B has correlation r= -0.65, then

a. the points in A exhibit a stronger linear association than B.

b. the points in B exhibit a stronger linear association than A.

c. neither A nor B has a stronger linear association.

d. you can't tell which data set has a stronger linear association without seeing the data or seeing the scatterplots.

e. a mistake has been made-r cannot be negative.

c. neither A nor B has a stronger linear association.

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

a. The number of people showering in a college dorm and the water pressure in each shower.

b. The outdoor temperature and the number of fans running in non-air conditioned dorm rooms.

c. The comfort rating of a mattress and the number of hours of uninterrupted sleep obtained.

d. The price of a home and its square footage.

e. The fuel efficiency of a car (miles per gallon) and its speed.

a. The number of people showering in a college dorm and the water pressure in each shower.

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

a. A straight line is not a good model for the data.

b. The correlation must be 0.

c. The correlation must be positive.

d. Outliers must be present.

e. The regression line might or might not be a good model for the data, depending on the extent of the curve.

a. A straight line is not a good model for the data.

Two variables, an explanatory variable x and a response variable y, are measured on each of several individuals. The correlation between these variables is found to be 0.88. To help us interpret this correlation, we should do which of the following?

a. Compute the least-squares regression line of y on x and consider whether the slope is positive or negative.

b. Interchange the roles of x and y (ie, treat x as the response variable and y as the explanatory variable) and recompute the correlation.

c. Plot the data.

d. Determine whether x or y has larger values before computing the residuals.

e. All of the above.

c. Plot the data.

If removing an observation from a data set would have a marked change on the position of the LSRL, fit to the data, what is the point called:

a. Robust

b. A residual

c. A response

d. Influential

e. None of the above

d. Influential