Download Math 92: Review for Final Module 1 Distinguish between an

Math 92: Review for Final
Module 1
Distinguish between an observational study and an experiment
Distinguish between categorical and quantitative variables
Determine which kinds of studies/experiments establish cause-effect and which ones don’t
Recognize confounding variables in a study or experiment
Identify the sampling plan for a study. Recognize implications and limitations of the plan.
Identify features of experiment design that control the effects of confounding. (direct control, random
assignment, blinding, placebos)
Identify explanatory and response variables
Explain how a sample can be biased
Module 6 – probability
compute simple probabilities (example, picking marbles at random out of a bag, rolling dice, flipping
coins)
Law of large numbers
Make a probability distribution
Know the difference between discrete and continuous random variables
Module 6 – Normal curve
sketch a normal curve
Use the 68-95-99.7 rule
z-scores
Use the table
Module 4
Know the formula y = abx, and know what “a” and “b” represent
Know the difference between linear and exponential
Sample Questions
For questions 1-4, use the following information: A medical doctor has forty patients with high
cholesterol issues. She wants to compare the effectiveness of two high cholesterol treatments. To make
her comparison, she randomly assigns 20 patients to receive treatment 1. She gives the remaining 20
patients treatment 2.
1. (Multiple choice) What type of study design is this?
a. Observational study
b. Sample survey
c. Experiment
2. List at least two possible confounding variables in this study/experiment:
3. The explanatory variable is_______________________________
4. Explain why it is necessary to randomly assign the individuals to each group.
5. Which of the following is true about the use of sample surveys?
a. Everyone in the population must also be in the sample.
b. The population is a subset of the sample.
c. Data from people in the population are used to gain information about the sample.
d. Data from people in the sample are used to gain information about the population.
6. Which one of the following variables is a categorical variable?
a. Number of ear piercings a person has
b. Height of a person measured in inches
c. Weight of a person measured in pounds
d. Yes or No vote for the legalization of marijuana
7. In June 2011 CBS News and the New York Times reported the results of a poll about problems and
priorities for the U.S. In the poll 979 U.S. adults answered the question, “What do you think is the most
important problem facing this country today?” From a list of options, 53% of those polled said
“economy/jobs.”
This is an observational study designed to answer a question about a population. Who is the population?
a) the 979 U.S. adults polled
b) U.S. adults who watch CBS News or read the New York Times
c) the 53% who answered “economy/jobs”
d) all U.S. adults
8. The website “www.abcnews.com” posted the following online poll:
“do you agree with the latest ‘Dancing with the Stars’ elimination? (yes, no)
3,000 people voted, and over 90% responded “yes”.
Explain why this sample of 3,000 people is a biased sample. Give at least two reasons.
9. Suppose a student has a 70% chance of answering a question correctly on a test.
a) What is the probability that he or she will answer all 3 of the questions correctly? (out of 3
questions)
10. Wildlife biologists believe the weights of adult trout can be described by a normal model. They collect
data from fishermen, and find that the mean weight is 2.8 kilograms, and the standard deviation is 0.6
kilograms.
a) Sketch the graph of the normal curve. Include 3 standard deviations above and below the mean.
b) Use the 68-95-99.7 rule to estimate the percentage of trout that weigh less than 2.2 kg.
c) if a trout weighed 1.2 kilograms, what would be its z-score?
d) What percentage of trout weigh more than 4.0 kg?
e) What percentage of trout weigh between 2.0 and 3.0 kg?
11) In a large bag of candy, 30% of the pieces are green, 20% of the pieces are red, and the rest are white.
a) What is the probability that a randomly chosen piece is white?
b) What is the probability that a randomly chosen piece is not red?
c) If you chose two pieces at random, what is the probability that both are red?
12. Make a probability distribution for flipping two coins. Let X = the number of heads
13) For each of the following, write E.G. (for exponential growth), ED (for exponential decay) or L (for
linear)
a) y = 80(1.5)x
b) y = 80 + 4x
c) y = 2x
d) y = 100 – 1.04x
e) y = (0.7)x
f) y = 56.89(0.93)x
g)
y
x
h)
y
x
14) Suppose, in the year 2000, there were 20 million music CDs sold in the U.S., and the number of
music CDs sold decreases at a rate of 5% each year.
a) Write an equation for the number of music CDs sold, x years after 2000.
b) Use the equation from part (a) to predict the number of music CDs that will be sold in the year 2015.
c) If there were 20 million music CDs sold in the year 2000, and the number decreased by 2 million per
year, would this be modeled by an exponential or linear equation? Explain. Write an equation.
15. Amanda’s little sister, Katie, is in high school. She recently had to take semester exams. Her scores
are in the table. Katie is upset because she thinks she did the worst in math but it is usually her best
subject! Which of the following statements is true about her scores?
Subject
Mean Score
Deviation
Katie’s Score
English
70
7
77
History
83
6
80
Math
60
5
70
Science
85
8
85
a. Katie did worse in English since that standard deviation is larger than the rest.
b. The score of 70 on math is a really good score since it’s 2 standard deviations above the mean
score.
c. The score of 85 in science is the “best” score since it is the highest score and not below the mean.
d. The score of 80 on History is the most impressive performance since it is close to the mean score.
16. On a national standardized exam, the scores follow a normal distribution with a mean of 60 and a
standard deviation of 13. What is the probability that a student will receive a score between 73 and 86?
a.
Less than 3%
b. 13.5%
c. 47.5%
d. 68%
17. Professor Lopez has a newly collected data set. The data set is normally distributed. The mean of the
data is 102 and the standard deviation is 11. Within what interval will 68% of the data fall?
a. (91, 113)
b. (102, 113)
c. (102, 124)
d. (80, 124)
Answers
1. B
2. answers will vary. Some possible answers are: age, sex, ethnicity, diet, exercise
3. the treatment
4. random assignment is neccessary so each group is similar
5. D
6. D
7. D
8. This is a volunteer response sample. Those with strong feelings are over-represented in this sample.
Also, those who read
abcnews.com are over-represented in the sample
9. 0.343
10a.
10b. 16%
10c. -2.67
10d. 2.5% (2.2% is also acceptable)
10e. 53.9%
11a. 50%
11b. 80%
11c. 0.04
12.
X
P
0
0.25
1
0.50
2
0.25
13a. EG. b. L. c. EG. d. L.
x
e. ED. f. ED. g. EG.
h. ED
14a. y = 20(0.95) . (million CDs). b. 9.266 million CDs.
15. B
16. B
17. A
c. linear. y = 20 – 2x