Download Partner Activity Rubric chapters 3,2,1

11/7/16
AP Statistics
Chapters 1 – 3 Partner Review
Statisticians:
Grade this_____
1. A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat in grams
gave the following results: predicted calories = 97.1053 + 9.6525(fat). Which of the following
statements 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 grams 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. If one cereal has 140 calories and 5 grams of fat, its residual is about 5 calories.
2. In a particular approximately normally distributed data set,
900. What is the mean of the data set?
A.
B.
and 9.18% of the data fall below
C.
D.
E.
3. A cumulative frequency graph for the 48 racers who finished
the grueling 50km cross country ski race at the 2010 Vancouver
Olympics is shown. Approximately what proportion of the
racers finished the race in more than 2.15 hours?
A. 0.17
B. 0.40
D. 0.50
C. 0.45
E. 0.55
4. Which of the following statements are true?
I.
Correlation and regression require that there are clearly defined explanatory and response
variables.
II. Scatterplots require that both variables be quantitative.
III. Every least squares regression line passes through the point ( x , y ) .
A. I and II only
D. I, II, and III
B. I and III only
E. None are true
C. II and III only
5. Which measures of center and spread are most
appropriate to describe the histogram shown?
A.
B.
C.
D.
E.
mean and standard deviation
mean and interquartile range
mean and range
median and interquartile range
median and standard deviation
6. Data on the diameter (in inches) and the age (in years) of a sample
of 25 oak trees yielded the regression equation ̂ = 1.18 + 0.165 x ,
where ̂ is diameter and x is age. The residual plot for the
regression is shown.
Which of the following is the best explanation of the relationship
between growth in diameter and age of tree?
A. The diameter grows at about 0.165 inches per year throughout the life of the tree.
B. The diameter grows slower than 0.165 inches per year early in the life of the tree and faster than
0.165 inches per year later in life, then slower in the last few years.
C. The diameter grows faster than 0.165 inches per year early in the life of the tree and slower than
0.165 inches per year later in life, then faster in the last few years.
D. The diameter grows at a rate of 1.18 inches per year throughout the life of the tree.
E. The diameter grows slower than 1.18 inches per year early in the life of the tree and faster than 1.18
inches per year later, then slower in the last few years.
7. For a given company, the scatterplot of log(number of employees) versus calendar year from 1990
through 2010 shows a strong, positive, linear pattern. The residual plot for the transformed data shows
no pattern. Which of the following conclusions can be drawn from this information?
A. The scatterplot of log(number of employees) versus log(calendar year)will also be strong, positive,
and linear.
B. The relationship between number of employees and calendar year can be modeled well by an
exponential function.
C. The relationship between number of employees and calendar year can be modeled well by a power
function.
D. The relationship between number of employees and calendar year can be modeled well by a linear
function.
E. The number of employees at the company in 2020 can be predicted accurately by the linear
regression of log(number of employees) versus calendar year from this data.
For free response questions, show all work to receive full credit.
8. (2013 #4 audit) A taxicab company in a large city charges passengers a flat fee to enter a cab plus an
additional fee per mile. There is also a charge for time spent stopped in traffic. The company wants to
develop a new method for determining fares based on mileage and a flat fee only, not on time spent
stopped in traffic. A random sample of 10 recent cab fares was selected, and the distance, in miles, and
the fare, in dollars, were recorded. A regression model was fit to the data, and the output, scatterplot,
and residual plot are given below.
A. State the equation of the least squares regression line for these data. Define any variables used in the
equation.
B. Is a linear model appropriate to use for these data? Explain your response.
C. Interpret the value of r2 in the context of this problem.
D. If this equation were used to predict the cost of a 2.2 mile cab ride, would the prediction be too
large or too small? Explain your reasoning and show your calculations.
A. The regression line equation is
traveled in miles.
yˆ  4.296  1.229x where ŷ is the predicted taxi fare in dollars and x is the distance
B. The linear model is appropriate because the scatterplot shows a strong, positive linear association and the residual plot
shows no pattern. The residuals are widely scattered about x = 0.
C. r2 = 0.873 Approximately 87% of the variation in taxi fare, measured in dollars, is accounted for by the LSRL with distance
in miles as the explanatory variable.
D. The prediction would be too large. The data value on the scatterplot for x = 2.2 is below the regression line, and the residual
for x = 2.2 is negative. Therefore y  yˆ , the residual, indicates that the predicted y value is greater than the actual y value.
9. (2010 #1) Agricultural experts are trying to develop a bird deterrent to reduce costly damage to crops
in the United States. An experiment is to be conducted using garlic oil to study its effectiveness as a
nontoxic, environmentally safe bird repellant. The experiment will use European starlings, a bird
species that causes considerable damage annually to the corn crop in the United States. Food granules
made from corn are to be infused with garlic oil in each of five concentrations of garlic – 0 %, 2%,
10%, 25%, and 50%. The researchers will determine the adverse reaction of the birds to the repellant
by measuring the number of food granules consumed during a two-hour period following overnight
food deprivation. There are forty birds available for the experiment, and the researchers will use eight
birds for each concentration of garlic. Each bird will be kept in a separate cage and provided with the
same number of food granules.
A. For the experiment, identify:
i. the treatments
ii. the experimental units
iii. the response that will be measured
B. After performing the experiment, the researchers recorded the data shown in the table.
i. Using the grid below, construct a graph of the data that could be used to investigate
the appropriateness of a linear regression model for analyzing the results of the
experiment.
ii. Based on your graph, do you think a linear regression model is appropriate? Explain.