AP Statistics Optional Review Midterm
Name: ____________________________
1. An experiment was performed to determine the effectiveness of a new drug designed to reduce cholesterol.
To analyze the results, a regression line was calculated using x = dosage (mg) and y = cholesterol reduction.
Partial output from computer software is provided below.
Term
Intercept
Dosage
Estimate
1.3888889
0.6366667
Std Error
8.468871
0.131199
t Ratio
0.16
4.85
Prob>|t|
0.8744
0.0019
Calculate the residual for a subject who took a 100 mg dose and had a cholesterol reduction of 50.
a. 90
b. -90
c. 15
d. -15
e. Cannot be determined from the given information
3. Estimate the standard deviation of this distribution:
a. 5
b. 10
c. 20
d. 50
e. 75
75
50
25
10 20 30 40 50 60 70 80 90 10 0
Coun t Axis
2. Does color affect appetite? To investigate this question, two researchers recruited 20 student volunteers and
told them they were doing a study on a new television program. While the students were watching the program,
the researchers gave each of the students a bag of popcorn. However, half of the bags were red and the other
half were blue. When the show was over, the researchers collected the bags and measured the amount of
popcorn remaining. Which of the following is the explanatory variable in this study?
a. The color of the bag
b. The initial amount of popcorn
c. The television program
d. The amount of popcorn left in the bags
e. The 20 student volunteers
12 0
4. A study was conducted to measure the endurance of athletes by measuring how long each athlete can run on
a treadmill without stopping. The amount of time that the athlete runs on the treadmill is:
a. a categorical variable
b. a continuous numerical variable
c. a discrete numerical variable
d. a confounding variable
e. an explanatory variable
5. Suppose that you wanted to estimate the average height of students at your high school. Which would be the
least useful variable for stratification?
a. gender
b. grade
c. shoe size
d. age
e. grade point average
6. The following stemplot displays the weights (in pounds) of a random sample of 20
men. What is the interquartile range of this data?
a. 40 pounds
b. 47 pounds
c. 33 pounds
d. 16.5 pounds
e. 77 pounds
Men’s Weights
13 26
14 18
15 289
stem = tens
16 477
leaf = ones
17 136
18
19 019
20 2269
7. Does taking Algebra 2 increase SAT scores? To answer this question, the math department of a local high
school randomly selected 50 students and classified them into two groups: those who have taken Algebra 2 and
those who haven’t. The average SAT score for the group who had taken Algebra 2 was significantly higher
than the average SAT score for the group that didn’t have Algebra 2. Based on this study, which is the most
appropriate conclusion?
a. Taking Algebra 2 caused an increase in SAT scores for all students in the school.
b. Taking Algebra 2 caused an increase in SAT scores, but only for the 50 students in the study.
c. Taking Algebra 2 is associated with higher SAT scores for the entire school, but taking Algebra 2
didn’t necessarily cause the increase.
d. Taking Algebra 2 is associated with higher SAT scores for the 50 students in the study, but taking
Algebra 2 didn’t necessarily cause the increase.
e. None of these conclusions are appropriate.
8. Suppose that one the most recent test in your statistics class, the mean grade was 71 points with a standard
deviation of 13 points. Your teacher, being extremely merciful and kindhearted, decided to add 5 points to
every students’ score. What are the new mean and standard deviation?
a. mean = 76, standard deviation = 18
b. mean = 71, standard deviation = 18
c. mean = 71, standard deviation = 13
d. mean = 76, standard deviation = 13
e. we cannot find the mean and standard deviation without the individual test scores
9. Earthquake intensities are measured using a device called a seismograph, which is designed to be most
sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements
of nine earthquakes gave the following readings:
4.5 L 5.5 H 8.7 8.9 6.0 H 5.2
where L indicates that the earthquake had intensity below 4.0 and an H indicates that the earthquake had
intensity above 9.0. The median earthquake intensity of the sample is:
a. 8.70
b. 5.75
c. 6.00
d. 6.47
e. Cannot be computed since all of the values are not known
10. Some descriptive statistics for a set of test scores are shown above. For this test, a certain student had a
standardized score of z = -1.2. What score did this student receive on the test?
a. 266.28
N
Mean
Median
TrMean StDev
b. 779.42
50
1045.7
1024.7
1041.9
221.9
c. 1008.02
SE Mean Minimum Maximum
Q1
Q3
d. 1083.38
31.4
628.9
1577.1
877.7
1219.5
e. 1311.98
11. A tomato farmer has decided to design an experiment to determine the effect of a certain fertilizer on the
production of his tomato plants. He has a rectangular plot available that will fit 20 tomato plants (see diagram
below) and wants to use 5 different levels of fertilizer (0, 1, 2, 3, 4 ounces per plant per week).
a. Explain to the farmer how he should assign the 5 treatments to the 20 tomato plants in the field using a
completely randomized design.
b. What is the purpose of randomization in this experiment?
c. Was replication used correctly in this experiment? Explain.
After conducting this experiment for three months, the farmer calculates the total production of each plant
(measured in pounds). This information is summarized in the output below.
The regression equation is
Tomatoes (pounds) = 10.4 + 1.85 Fertilizer (ounces)
Predictor
Constant
Fertilizer (ounces)
S = 1.78590
Coef
10.3500
1.8500
R-Sq = 70.5%
SE Coef
0.6917
0.2824
P
0.000
0.000
R-Sq(adj) = 68.8%
Scatterplot of Tomatoes (pounds) vs Fertilizer (ounces)
Residuals Versus Fertilizer (ounces)
(response is Tomatoes (pounds))
20.0
3
2
17.5
1
Residual
Tomatoes (pounds)
T
14.96
6.55
15.0
12.5
0
-1
-2
10.0
-3
-4
0
1
2
Fertilizer (ounces)
3
4
0
1
2
Fertilizer (ounces)
3
4
d. Is a linear model appropriate for this data? What information tells you this?
e. Interpret the slope of the least squares regression line in the context of the question.
f. Interpret the standard deviation in the context of the question.
g. Predict the average yields for plants given 7.5 ounces per plant per week. Are you confident in this
prediction? Explain.
h. Here is a boxplot and histogram of the residuals. Briefly describe this distribution.
Histogram of the Residuals
(response is Tomatoes (pounds))
5
Frequency
4
3
2
1
0
-3
-2
-1
0
Residual
1
2
3
i. If a farmer decided to use 2.5 ounces of fertilizer per plant per week on all of his plants, between what 2
values would you expect to find most of weights? Explain your reasoning.