Download STT 200 Sample Problems for Test 2

STT 200 Sample Problems for Test 2
1. Many studies are trying to find a cure for chronic back pain. In one such study, a
physician is comparing the medication currently being used (drug A) to a newly
developed drug (drug B). Seventy-three volunteers, suffering from chronic back pain, are
participating in this study. The physician’s assistant has a list of all 73 subjects and
randomly divides the subjects into two groups. Group 1 will receive drug A and group 2
will receive drug B. The assistant is the only one who knows to which group the subjects
have been assigned. The physician monitors the subjects over a 2 month period and the
amount of improvement is recorded. What type of study is this?
A) An observational study.
B) An experiment, but not a double-blind
experiment.
C) A double-blind experiment.
D) A survey.
2. A market research company wishes to find out which of two internet search engines
the population of students at a university prefers to use: Google or MSN Search. A
random sample of students is selected, and each one is asked to search for a certain
subject using Google and then MSN, or vice versa. The order of the two searches was
determined at random. They then indicate which internet search engine they prefer.
What type of study is this?
A) An observational study. B) An experiment, but not a double-blind experiment.
C) A double-blind experiment.
D) A survey
3. Sickle-cell disease is a painful disorder of the red blood cells that in the United States
affects mostly blacks. To investigate whether the drug hydroxyurea can reduce the pain
associated with sickle-cell disease, a study by the National Institutes of Health gave the
drug to 150 sickle-cell sufferers and a placebo to another 150. The researchers then
counted the number of episodes of pain reported by each subject. What is the response
variable in this study?
A) The drug hydroxyurea.
B) The number of episodes of pain.
C) The presence of sickle-cell disease.
D) The number of red blood cells.
4. Seventy-five college students are taking part in a study initiated by a large computer
manufacturer. The company is designing a new type of laptop computer and has created
prototypes of it with two different keyboard designs. They are also including the current
design of the laptop in the experiment. Each of the students was randomly assigned to
one of the three types of computers. The students are asked to spend 15 minutes on one of
the computers performing several tasks (typing words, numbers, making corrections,
etc.). The ease of use of the keyboard was then rated on a five-point scale by having the
students fill out a short questionnaire. Which of the following basic principles of
statistical design was not used in this experiment?
A) control
B) randomization
C) repetition
A group of college students believes that herbal tea has remarkable restorative powers.
To test its theory, the group makes weekly visits to a local nursing home, visiting with
residents, talking with them, and serving them herbal tea. After several months, many of
the residents are more cheerful and healthy.
5. What is the explanatory variable in this experiment?
A) The emotional state of the residents.
C) The fact that this is a local nursing home.
B) Herbal tea.
D) The college students.
6. Olivia is planning to take a foreign language class. To research how satisfied other
students are with their foreign language classes, she decides to take a sample of 20 such
students. The university offers classes in four languages: Spanish, German, French, and
Japanese. She will select a simple random sample of five students from each language.
What sampling technique is Olivia using?
A) A simple random sample.
B) A multistage sample.
C) A stratified sample.
D) None of the above.
Use the following to answer questions 7 & 8: A standard deck of cards has 52 cards. The
cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have
one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards
are clubs (black), and 13 cards are spades (black).
7. One card is selected at random and the denomination is recorded. Which of the
following is the correct sample space S for the set of possible outcomes?
A) S = {red, black}
B) S = {red, red, black, black}
C) S = {hearts, diamonds, clubs, spades}
D) S = {red, black, hearts, diamonds, clubs,
spades}
8. Two cards are selected at random and the color is recorded. Which of the following is
the correct sample space S for the set of possible outcomes?
A) S = {red, black}
B) S = {(red, red), (red, black), (black, red), (black, black)}
C) S = {0, 1, 2}
D) S = {red, black, hearts, diamonds, clubs, spades}
Use the following to answer questions 9-11: Let the random variable X be the number of
repair calls that an appliance repair shop may receive during an hour. The distribution of
X is given below.
Value of X
0
1
2
3
4
Probability
0.2
k
3k
2k
0.2
9. What is the value of k?
A) 0.1
B) 0.2
C) 0.02
D) 0.3
10. What is the probability that the repair shop receives at least three repair calls during
an hour?
A) 0.18
B) 0.2
C) 0.80
D) 0.40
11. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3.
What is P(A and B)?
A) 0.09
B) 0.51
C) 0.52
D) 0.60
12. What is P(A or B)? Use the result from 11.
A) 0.09
B) 0.51
C) 0.52
D) 0.60
In a large city, 72% of the people are known to own a cell phone, 38% are known to own
a pager, and 29% own both a cell phone and a pager.
13. What proportion of people in this large city own either a cell phone or a pager or
both?
A) 0.29
B) 0.67
C) 0.81
D) 1.1
14. What is the probability that a randomly selected person from this city owns a pager,
given that the person owns a cell phone?
A) 0.266
B) 0.38
C) 0.403
D) 0.528
A multiple choice test consists of 5 questions. For each question there are 4 choices from
which the answer is selected. A student guesses the answer for each question.
15. What is the probability that he gets exactly all 5 questions right?
16. What is the probability that he gets at least 1 question right?
17. Two cards are selected at random and the denomination is recorded. The event H is
defined as the event that the first card is clubs. Which of the following correctly defines
event H?
A) H = {clubs, diamonds, hearts, spades}
B) H = {hearts, diamonds, clubs, spades}
C) H = {(clubs, diamonds), (clubs, hearts), (clubs, spades)}
D) H = {(clubs, diamonds), (clubs, clubs), (clubs, spades), (clubs, hearts)}
18. A college basketball player makes 75% of his free throws. Assume free throws are
independent. What is the probability that he makes all of his next six free throws?
19. In order to assess the opinion of employees at a software company, a researcher
interviews the first fifteen employees he meets who are willing express their opinion.
This a simple random sample (SRS). SAY TRUE OR FALSE
20. In a study to assess whether aspirin reduces the risk of a pregnant woman developing
hypertension, 34 pregnant women were randomly assigned to receive a low dosage of
aspirin every day while 31 pregnant women received a placebo every day. Of those in the
aspirin group 4 developed hypertension during their pregnancy, compared to 11 of those
in the placebo group.
i) Identify the explanatory variable in this study.
ii) Identify the response variable in this study.
ANSWER KEY
1. B
2. B
3. B
4. C
5. B
6. C
7. C
8. B
9. A
10. D
11. A
12. B
13. C
14. C
15. 0.00097
16. 0.763
17. D
18. 0.1779
19. B
20.
i) aspirin
ii) Developing hypertension