Math 135 Review Test 2 (Ch. 3, 4, & 5)
Part I – Multiple Choice
1. A statistician employed in a corporation believes that employees who receive better than average
increases tend to stay with the company longer. He based his conclusion on reports executed against the
employee historical database. This study is an example of
a) anecdotal evidence
b) an observational study based on available data
c) an observational study based on a sample survey
d) an experiment
2. Does drinking coffee help students learn better? A random sample of students at a university is
selected and each one is asked whether or not they have performed better on an exam after drinking
coffee. This study is an example of
a) anecdotal evidence
b) an observational study based on available data
c) an observational study based on a sample survey
d) an experiment
3. Both my grandmother and my mother have been drinking green tea for years. Both of them exhibit a
calm collected demeanor. I begin drinking green tea in the hopes that it will produce a calming effect on
my turbulent personality. My decision to start drinking green tea is based on
a) anecdotal evidence
b) an observational study based on available data
c) an observational study based on a sample survey
d) an experiment
4. Does shark fin extract help the symptoms of chronic fatigue syndrome? 12 people who suffer from the
syndrome participate in the study. Half of the volunteers are to be given shark fin extract twice a day and
the other half a placebo twice a day. The volunteers are checked for symptoms on a regular basis
throughout the study. The volunteers do not know if they were given the placebo or the extract and
neither does their doctor. This study is an example of
a) a double-blind experiment
b) anecdotal evidence
c) a single-blind experiment
d) an observational study
5. A television station is interested in predicting whether voters are in favor of an increase in the state
sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase
in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who
phoned in, 1474 (55.98%) were opposed to the increase. The number 55.98% is
a) a statistic
c) a sample
b) a parameter
d) a population
6. In the previous sample, the type of sample obtained is:
a) a simple random sample
c) a stratified sample
b) a voluntary response sample
d) a cluster sample
7.The process of taking information from a sample to draw conclusions about a population is called
a) random sampling
c) probability
b) statistical inference
d) John Jacob Jingle Heimer Schmidt
8. A group of University of South Florida surgery researchers believe that the drug aprotinin is effective
in reducing the blood loss of burn patients who undergo skin replacement surgery. In a clinical trial of 16
burn patients, the patients were first divided into groups (those who were severely burned and those who
had moderate or mild burns). Each group was then randomly assigned to receive aprotinin or a placebo
and the results were compared. This is an example of
a) An experiment using a completely randomized design
b) An observational study using available information
c) An experiment using multi-stage sampling
d) An experiment using randomized block design
9. Of the survey questions below, circle any that are certain to produce a biased response:
a) Does your business have an e-commerce strategy?
b) Do you think that interest groups should be allowed to give huge sums of money to
presidential candidates?
c) Do you support or oppose the proposed tax re-assessment for the city of Troy ?
d) Do you support capital punishment or do you feel that taking a human life is considered cruel
and unusual punishment?
10. If a fair die is thrown many times, the proportion of 2’s that are rolled will gradually approach what
value?
a) 2/6
c) 1/2
b) 1/6
d) none of the above
11. A new assessment survey is to be distributed to faculty. A random sample of departments is selected
and everyone in the department is included in the sample. This scenario is an example of which sampling
design?
a) stratified sampling
c) multi-stage sampling
b) cluster sampling
d) systematic sampling
12. A study is conducted to determine whether the average blood pressure for Americans has increased
over the past 10 years. A simple random sample (SRS) of 50 people is selected and their average blood
pressure is calculated. The average blood pressure for the 50 people is a _________________. The true
unknown mean blood pressure for all Americans is a _____________.
Part II
1. Can you increase the response rate for a mail survey by contacting the respondents before they
receive the survey? A study designed to address this question compared 3 groups of subjects.
The first group received a preliminary letter about the survey, the second group was phoned and
the third received no preliminary contact. A positive response was defined as returning the
survey within 2 weeks. (from James E. Stafford, “Influence of preliminary contact on mail
returns”, Journal of Marketing Research).
Intervention
Response
Letter
Phone Call
None
Yes
171
146
118
No
220
68
455
a. Identify the explanatory and response variables
b. Construct appropriate graphs to attempt to determine if there appears to be a relationship
between Intervention Type and Response.
c. Describe the relationship you see from the graphs (if any appears to exist).
2. Select an SRS of size 5 from a population of 450 people. Use line 131 from the Random Number
Table (T4). List the 5 ID’s selected below:
3. Does massage enable the muscles of tired athletes to recover from exertion faster than usual? To
answer this question, researchers recruited 8 amateur boxers and 8 amateur soccer players to
participate in an experiment. Researchers wanted to determine if there was a different in how the
boxers reacted to how the soccer players reacted? After a 20 minutes workout, each athlete was
randomly assigned to receive a massage or not. The heart rate and blood lactate levels were used
to measure whether the athlete “recovered” from the exertion.
Outline the design for this experiment (use “sport type” as the blocking variable) and then
perform the randomization necessary to put the subjects into groups (starting with line
125 in the table of random digits).
Boxers
1. Hanson
2. Henry
3. Smith
4. Carlton
5. McLean
6. Hampshire
7. Maher
8. Tyson
Soccer Players
1. Clark
2. Jones
3. James
4. Conner
5. Davies
6. Moller
7. Moses
8. Jannis
4. Choose an employee at random from a company and observe their annual salary. The table
below shows the probability of each salary category in this company:
Salary (in
< 25
25-49
50-75
>75
thousands)
Probability
0.09
0.54
0.36
??
b) Find the ?? probability.
c) Find the probability that the random person selected has a salary that is < $50,000.
d) Let A be the event that a person makes less than $25,000. Describe the event Ac in words and
then find the probability of Ac
e) Suppose 2 employees are selected at random. Assuming independence, what is the probability
that both employees make less than $25,000? That one employee makes less than $25,000 and
one does not? (Assume that order matters).
5. Suppose in a married couple the probability that the wife smokes is 0.24 and the probability that
the husband smokes is 0.32. The probability that both the husband and the wife smoke is 0.18. A
married couple is selected at random.
a. Find the probability that either of them smokes.
b. Find the probability that neither of them smokes.
c. What is the probability that the husband does not smoke?
6. Consider the following probability distribution:
X
−2
0
Probability of X
0.03
0.25
a.
b.
c.
d.
1
0.4
X is what type of random variable in this example?
Is this a valid probability distribution? How do you know?
Find P(X < 1)
Find P(X ≥ 0)
2
0.32
7. Let X represent a number that is randomly generated between 0 and 8. X is a continuous random
variable.
a. Draw a picture of the probability distribution of X (the “rectangle”)
b. Find P(X > 5.2)
c. Find P(0.3<X<2.6)
8. A population has a mean of 500 and a standard deviation of 30. Many random samples are
selected from the population (all with 36 items).
a. Find the mean of the sampling distribution for x . That is, find  x .
b. Find the standard deviation for the sampling distribution for x .
c. What is the shape for the sampling distribution for x ? What theorem allows you to draw
this conclusion?
9. WageWeb provides compensation information and services on more than 160 positions. As of
October 1, 2003, the national average salary for a registered nurse (RN) was $47,858. Suppose
the standard deviation is $7750.
a. Find the probability that the sample mean for 100 randomly selected nurses is less than
$45,000.
b. Find the probability that the sample mean for 50 selected nurses is greater than $50,000.
10. According to a CNN report, 7% of the population do not have traditional phones and instead rely
only on cell phones. Suppose a random sample of 750 telephone users is obtained.
a. Describe the sampling distribution for p̂ , the sample proportion that are “cell-phone
only”.
b. In a random sample of 750 telephone users, what is the probability that more than 8% are
“cell-phone only”?
c. Would it be unusual if a random sample of 750 adults results in 40 or fewer being “cellphone only”
11. Suppose we know that the weight of male runners in the U.S. conform to a Normal distribution
with a mean of 150 pounds and a standard deviation of 15 pounds. A runner is selected at
random.
a. What is the probability that the runner’s weight is less than 135 pounds?
b. What is the probability that the runner’s weight is greater than 160 pounds?
c. What is the probability that the runner’s weight is between 140 and 160 pounds?
d. Suppose a random sample of 10 runners is selected. What is the probability that the
sample mean for the ten runners is less than 135 pounds? Would this be considered an
unusual event?
Math 135 Review Test 2
Answer Key
Part I: Multiple Choice
1. b
2. c
3. a
4. a
5. a
6. b
7. b
8. d
9. d
10. b
11. b
12. statistic; parameter
Part II:
1.a) E-Intervention Type R-Response
b) Conditional Distribution of Response given Intervention:
Letter: Y 44% N 56%
Phone Call: Y 68% N 32%
None: Y 21% N 79%
c) In general, intervention via phone call seemed to produce the best response rate
2. ID’s: 050, 071, 281, 194, 148
3. Will cover in class
4. b) 0.01 c) 0.63
d) Person makes at least $25,000; 0.91 e) 0.0081; 0.1638
5. a) 0.38
b) 0.62
c) 0.68
6. a) discrete b) yes; probabilities are all between 0 and 1 (inclusive) and the probabilities sum
to 1
c) 0.28
d) 0.97
7. a) rectangle with length of 8 and a height of 1/8
b) 0.35
c) 0.2875
8. a) 500
b) 30/sqrt(36) = 5
c) Normal; Central Limit Theorem
9. a) z-score “off the chart” on the low side; probability is < 0.0002 which means it is
essentially zero (or very close to zero)
b) 0.0256
10. a) distribution for p-hat is Normal with a mean of 0.07 and a standard deviation of
approximately 0.009317
b) 0.1423
c)0.0367
11. a) 0.1587 b) 0.2514
c) 0.4972
d) 0.0008; highly unusual