Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) A science instructor assigns a group of students to investigate the relationship between the pH of
the water of a river and its waterʹs hardness (measured in grains). Some students wrote these
conclusions: ʺthere was a very strong correlation of 1.45 between pH of the water and waterʹs
hardness.ʺ Is the calculation of the correlation appropriate?
A) No: correlation must be equal to 1.
B) No: correlation cannot be greater than 1.
C) Yes: the pH and the hardness of the water are data collected from the same river.
D) Yes: correlation can be greater than 1.
E) No: there is little or no association.
1)
2) A science instructor assigns a group of students to investigate the linear relationship between the
pH of the water of a river and its waterʹs hardness (measured in grains). Some students wrote
these conclusions: ʺMy correlation of -0.84 shows that there is almost no association between pH
of the water and waterʹs hardness.ʺ Is the interpretation of the correlation appropriate?
A) Yes: pH and hardness of water do not have the same units.
B) No: correlation is always positive.
C) No: a correlation of -0.84 shows a strong relation in a negative direction.
D) Yes: a correlation of -0.84 shows a weak relation in a negative direction.
E) No: the pH and the hardness of the water are data collected from the same river.
2)
3) A survey was conducted in 20 counties to determine the percentage of teenagers who had used
marijuana and other drugs. Data shown on the following scatterplot indicate a correlation of 0.966
between the percent of teens who have used marijuana and the percent who have used other
drugs. Describe the association.
3)
A) Strong linear relation in a positive direction
B) Weak linear relation in a positive direction
C) Strong nonlinear relation in a positive direction
D) No evidence of relation
E) Strong curved relation in a positive direction
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4) Adam would like to buy a used car, and collected several data to evaluate the best model (such as
age, price, weight, etc.) Thanks to a scatterplot, he established that the relation between age and
weight is somewhat linear. He calculated that the correlation between age and weight is 0.514.
Describe the association.
A) Weak linear relation in a positive direction
B) Strong linear relation in a positive direction
C) Weak linear relation in a negative direction
D) No evidence of relation
E) Weak linear relation
Answer the question appropriately.
5) A random sample of records of electricity usage of homes gives the amount of electricity used in
July and size (in square feet) of 135 homes. A regression was done to predict the amount of
electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear model is
4)
5)
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appropriate. The model is usage = 1266 + 0.7 size. Explain what the slope of the line says about the
electricity usage and home size.
A) On average, the amount of electricity used increases by 1266 kilowatt-hours when the size of
the house is increased by a square foot.
B) On average, the amount of electricity used is 0.7 kilowatt hours less than the size of the
house.
C) On average, the amount of electricity used increases by 0.7 kilowatt-hours when the size of
the house is increased by a square foot.
D) On average, the size of the house increases by 0.7 feet for every kilowatt-hour used.
E) On average, the size of the house increases by 1266 feet for every kilowatt-hour used.
6) A random sample of records of electricity usage of homes gives the amount of electricity used and
size (in square feet) of 135 homes. A regression to predict the amount of electricity used (in
kilowatt-hours) from size has an R-squared of 71.0%. The residuals plot indicated that a linear
model is appropriate. Write a sentence summarizing what R2 says about this regression.
6)
A) Size differences explain 71.0% of the variation in electricity usage.
B) Size differences explain 29% of the variation in electricity usage.
C) Differences in electricity usage explain 71.0% of the variation in the size of house.
D) Differences in electricity usage explain 29% of the variation in the number of house.
E) Size differences explain 71.0% of the variation in the number of homes.
Use the model to make the appropriate prediction.
7) A random sample of records of electricity usage of homes in the month of July gives the amount of
electricity used and size (in square feet) of 135 homes. A regression was done to predict the
amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear
^
model is appropriate. The model is usage = 1271 + 0.2 size. How much electricity would you
predict would be used in a house that is 2471 square feet?
A) 494.2 kilowatt-hours
B) 3742.2 kilowatt-hours
C) 1765.2 kilowatt-hours
D) 6000.00 kilowatt-hours
E) 776.8 kilowatt-hours
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7)
8) The relationship between the number of games won by a minor league baseball team and the
average attendance at their home games is analyzed. A regression analysis to predict the average
8)
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attendance from the number of games won gives the model attendance = -2000 + 187 wins.
Predict the average attendance of a team with 52 wins.
A) -1761 people
B) 7724 people
C) 9724 people
D) 11,724 people
E) 11 people
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the flaw(s) in the experiment or study described.
9) At St. Lukeʹs hospital in 1998, 674 women were diagnosed with breast cancer. Five years
later, 88% of the Caucasian women and 83% of the African American women were still
alive. A researcher concludes that being Caucasian causes women with breast cancer an
increased chance of surviving five years. Why is this conclusion not jusitified?
10) Researchers reported that going to the gym regularly increases your chance of finding a
high paying job. These findings were based on incomes reported by 200 active members of
a gym and 200 people who do not belong to a gym. Why is this conclusion not justified?
9)
10)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
11) The plastic arrow on a spinner for a childʹs game stops rotating to point at a color that will
determine what happens next. Determine whether the following probability assignment is
legitimate.
11)
Probability of ...
Red Yellow Green Blue
0.20 0.30 0.20 0.40
A) Legitimate
B) Not legitimate
12) In a business class, 35% of the students have never taken a statistics class, 10% have taken only one
semester of statistics, and the rest have taken two or more semesters of statistics. The professor
randomly assigns students to groups of three to work on a project for the course. What is the
probability that the first group mate you meet has studied two or more semesters of statistics?
A) 0.55
B) 0.10
C) 0.45
D) 0.65
E) 0.90
12)
13) In a business class, 35% of the students have never taken a statistics class, 10% have taken only one
semester of statistics, and the rest have taken two or more semesters of statistics. The professor
randomly assigns students to groups of three to work on a project for the course. What is the
probability that the first group mate you meet has studied some statistics?
A) 0.55
B) 0.45
C) 0.65
D) 0.10
E) 0.90
13)
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14) In a business class, 33% of the students have never taken a statistics class, 42% have taken only one
semester of statistics, and the rest have taken two or more semesters of statistics. The professor
randomly assigns students to groups of three to work on a project for the course. What is the
probability that the first group mate you meet has studied no more than one semester of statistics?
A) 0.25
B) 0.33
C) 0.58
D) 0.75
E) 0.42
14)
15) A consumer organization estimates that 30% of the households in a particular community have
one television set, 38% have two sets, and 20% have three or more sets. What is the probability that
a household chosen at random has no television sets?
A) 0.16
B) 0.12
C) 0.88
D) 0
E) 0.18
15)
16) A consumer organization estimates that 31% of the households in a particular community have
one television set, 39% have two sets, and 21% have three or more sets. What is the probability that
a household chosen at random has no more than one television set?
A) 0.48
B) 0.40
C) 0.31
D) 0.60
E) 0.09
16)
17) An Imaginary Poll in April 2005 asked 931 U.S. adults what their main source of news was:
newspapers, television, internet, or radio? Here are the results:
Response
Number
Newspapers 242
Television 398
Internet
126
Radio
165
Total
931
If we select a person at random from this sample of 931 adults, what is the probability that the
person responded ʺNewspapersʺ?
A) 0.242
B) 0.427
C) 0.135
D) 0.177
E) 0.260
17)
18) In a survey of American women who were asked to name their favorite color, 18% said blue, 15%
said red, 15% said green, 12% said yellow, 13% said black, and the rest named another color. If you
pick a survey participant at random, what is the probability that she named another color?
A) 0.27
B) 0.78
C) 0.73
D) 0.24
E) 0.20
18)
19) In a survey of American women who were asked to name their favorite color, 18% said blue, 19%
said red, 18% said green, 12% said yellow, 11% said black, and the rest named another color. If you
pick a survey participant at random, what is the probability that her favorite color is not blue?
A) 0.60
B) 0.72
C) 0.8
D) 0.18
E) 0.82
19)
Determine whether the events are disjoint, independent, neither, or both.
20) In rolling a fair die twice, the events of getting a 2 on the first roll and a 4 on the second
A) Disjoint
B) Independent
C) Neither
D) Both
20)
21) In filling out a ballot for president, the events of voting for the Democratic candidate and voting
for the Republican candidate
A) Disjoint
B) Independent
C) Neither
D) Both
21)
22) In driving a car, the events of driving over the speed limit and getting a speeding ticket
A) Disjoint
B) Independent
C) Neither
D) Both
22)
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List the sample space and tell whether the events are equally likely.
23) Toss a coin five times; record the number of heads.
A) {0, 1, 2, 3, 4, 5}, equally likely
B) {1, 2}, equally likely
C) {1, 2, 3, 4, 5}, equally likely
D) {0, 1, 2, 3, 4, 5}, not equally likely
E) {1, 2, 3, 4, 5}, not equally likely
24) Roll two dice; record the smaller number.
A) {1, 2, 3, 4, 5}, equally likely
B) {1, 2, 3, 4, 5}, not equally likely
C) {0, 1, 2, 3, 4, 5}, equally likely
D) {1, 2, 3, 4, 5, 6}, not equally likely
E) {1, 2, 3, 4, 5, 6}, equally likely
23)
24)
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Answer Key
Testname: REGRESSION SAMPLING PROB EXERCISES
1)
2)
3)
4)
5)
6)
7)
8)
9)
B
C
A
A
C
A
C
B
Since there is no random assignment, there is no way to know that being Caucasian causes women with breast cancer
an increased chance of surviving five years; there may have been lurking variables. For example, Caucasian women
may be more affluent and able to afford better health care or better nutrition. They may have a less stressful lifestyle,
or maybe they donʹt have to work as much. They may live in more affluent areas where there is less pollution and less
noise.
10) Since there is no random assignment, there is no way to know that going to the gym increases the chance of finding a
high paying job; there may have been lurking variables. For example, maybe people with high paying jobs are under
more stress and have more need to go to the gym. Or maybe those with high paying jobs are more likely to be able to
afford gym membership. Or another possibility, people who are more motivated and ambitious are more likely to find
a high paying job and more likely to go to the gym.
11) B
12) A
13) C
14) D
15) B
16) B
17) E
18) A
19) E
20) B
21) A
22) C
23) D
24) D
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