Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later,
88% of the Caucasian women and 63% of the African American women were still alive.
This observational study shows an association between race and breast cancer
survival– – that Caucasian women are more likely to survive breast cancer than African
American women. How could this study be modified to make it a designed experiment?
Comment on the feasibility of the designed experiment that you described.
1)
2)
A researcher wishes to assess the working conditions of farm workers at farms in his
district. There are 37 farms in the district which are widely scattered geographically. The
researcher wishes to interview at least 300 farm workers. Describe a method for selecting a
sample which involves cluster sampling. Each farm employs approximately 50 workers.
2)
3)
A tax auditor has a pile of 191 tax returns of which he would like to select 17 for a special
audit. Describe a method for selecting the sample which involves systematic random
sampling.
3)
4)
An agricultural researcher wishes to compare the yield of four different varieties of wheat.
64 plots of land are available for an experiment. On each plot of land one of the varieties of
wheat will be grown. At the end of the experiment the yield for the different varieties will
be compared. 32 of the plots are at one site (site A) and the other 32 are at another site (site
B). The soil at site A differs significantly from the soil at site B. If the researcher wishes to
design an experiment using completely randomized design, how could the wheat varieties
be assigned to the different plots?
4)
5)
Describe the steps involved when using stratified random sampling with proportional
allocation. What are the advantages of this sampling method?
5)
6)
In a designed experiment, explain the difference between the treatments and the factors.
6)
7)
An agricultural researcher wishes to compare the yield of four different varieties of wheat.
64 plots of land are available for an experiment. On each plot of land one of the varieties of
wheat will be grown. At the end of the experiment the yield for the different varieties will
be compared. 32 of the plots are at one site (site A) and the other 32 are at another site (site
B). The soil at site A differs significantly from the soil at site B. If the researcher wishes to
design an experiment using randomized block design, how could the wheat varieties be
assigned to the different plots?
7)
8)
Which method of sampling is easier: simple random sampling or systematic random
sampling?
8)
9)
Define probability sampling. Identify some advantages of probability sampling.
9)
10)
A college lecturer has devised a new method of teaching a particular mathematical concept
and wishes to try out this teaching method on a representative sample of his students.
There are 76 students in his class and he wishes to obtain a simple random sample of 25 of
them. Describe a method he could use to obtain the sample.
10)
11)
A college lecturer has devised a new method of teaching a particular mathematical concept
and wishes to try out this teaching method on a representative sample of his students.
There are 76 students in his class and he wishes to obtain a simple random sample of 25 of
them. Describe a method which would be unlikely to yield a representative sample.
11)
12)
Define observational study and experiment. Define the terms “treatment group” and
“control group” as part of your answer.
12)
13)
Fill in the following blanks: The two major types of statistics are ______________ statistics
and ___________ statistics.
13)
14)
Define the terms population and sample.
14)
15)
Define simple random sampling. Explain why this is important in design of experiments.
15)
16)
Describe a double–blind experiment and explain why blinding is used. Define the term
“placebo effect” as part of the answer.
16)
17)
The residents of one town are classified by a social scientist as follows.
Lower income: 4005
Middle income: 2047
Upper income: 2848
The scientist wishes to pick a sample of 200 of the residents for a study. Describe a method
for selecting the sample which involves stratified sampling with proportional allocation.
17)
18)
Describe the advantages and disadvantages of cluster sampling as compared with simple
random sampling.
18)
19)
A political researcher wishes to gauge political sentiment regarding a proposed tax cut. He
obtains a list of 1000 email addresses from an internet provider, uses a random number
table to select a random sample of 100 of these addresses, emails the people in the sample
and requests that they respond to his questions by email. Do you think that the group of
people who respond is likely to be representative of all registered voters? Explain your
answer.
19)
20)
A study was conducted to evaluate the effectiveness of a new diet pill for men. A group of
3000 men were involved in the study. Of these 3000 men, 2311 took the diet pill and 889
were given a placebo. Identify the treatments, the treatment group, and the control group.
20)
21)
Why do statisticians sometimes use inferential statistics to draw conclusions about a
population? In what situations might a statistician draw conclusions about a population
using descriptive statistics only?
21)
22)
Give an example of a designed experiment. In your experiment, identify the experimental
units, the response variable, the factor(s), the levels of each factor, and the treatments.
22)
23)
A store manager wishes to determine whether his customers would be prepared to pay a
little extra for organic produce. He uses a random number table to choose 50 random
numbers between 1 and 200. He stands outside the store on a Monday morning between
9:00 a.m. and 12:00 noon and interviews the people corresponding to the random numbers.
For example random number 82 would correspond to the 82nd person to arrive. Do you
think that the sample obtained in this way will be representative of all the store’s
customers?
23)
24)
Explain the difference between an observational study and a designed experiment.
24)
Use the random number table in Appendix A to obtain the required list of random numbers.
25)
A market researcher is conducting a telephone poll. She has a list of 581 registered voters
and wishes to interview a random sample of 12 of them. Construct a list of 12 random
numbers between 1 and 581 that can be used in obtaining the required simple random
sample. Use the random number table and use as your starting point the digits 432 in row
13, columns 10–12.
25)
Provide an appropriate response.
26)
The effects of global warming on the planet have received increased national attention in
recent years. But how many U.S. adults would be willing to change certain personal
behaviors in order to help reverse the effects of global warming? A major pollster
conducted a telephone poll of 1010 U.S. adults to determine the answer to the following
questions: (1) Is public transportation a viable option for you? (2) If not, do you own a
hybrid vehicle or one that gets more than an overall average of 30 miles per gallon? (3) If
not, would you be willing to purchase a hybrid vehicle within the five years? Respondents
were also asked questions about age, sex, race, education, region, and household income to
ensure that results represented a cross section of U.S. adults.
i) What kind of sampling design was used in this survey? Explain your answer.
ii) If 89% of the respondents answered the first question in the negative, what was the
approximate sample size for the second question?
iii) If 75% of those responding to the second question answered “no,” what was the
approximate size for the third question?
26)
Use the random number table in Appendix A to obtain the required list of random numbers.
27)
A company employs 5382 people and wishes to interview a random sample of 14 of them
with regard to the company‘s health insurance policy. Construct a list of 14 random
numbers between 1 and 5382 that can be used in obtaining the required simple random
sample. Use the random number table and use as your starting point the digits 0691 in row
3, columns 30–33.
27)
Provide an appropriate response.
28)
An education researcher wishes to assess the effectiveness of three different methods for
teaching young children to read. The 380 children participating in the study are divided
into three groups. The study runs for six months. The children in the first group are taught
using method A, the children in the second group are taught using method B, and the
children in the third group are taught using method C. At the end of the six months, the
reading ability of the children in the different groups is assessed. Why might
randomization be used when dividing the children into three groups?
28)
29)
Define the terms “stratified sampling”, “systematic sampling” and “cluster sampling”. Give
examples for each.
29)
Use the random number table in Appendix A to obtain the required list of random numbers.
30)
A magazine is awarding a cash prize for 10 winners in its competition. 470 of the
contestants have answered all the competition questions correctly. The magazine will pick
the 10 winners at random from among these 470 contestants. Construct a list of 10 random
numbers between 1 and 470 that can be used in obtaining the required simple random
sample. Use the random number table and use as your starting point the digits 270 in row
12, columns 5–7.
30)
Provide an appropriate response.
31)
An agricultural researcher wishes to compare the yield of four different varieties of wheat.
64 plots of land are available for an experiment. On each plot of land one of the varieties of
wheat will be grown. At the end of the experiment the yield for the different varieties will
be compared. 32 of the plots are at one site (site A) and the other 32 are at another site (site
B). The soil at site A differs significantly from the soil at site B. The researcher wishes to
design an experiment. In this example, why might a randomized block design, with
blocking by soil type, be preferable to a completely randomized design?
31)
32)
Define observational study and designed experiment.
32)
33)
In a clinical trial, each participant will receive a placebo, a low dosage of a drug, or a high
dosage of the drug. The participants consist of 90 men and 90 women. The 90 men are
randomly divided into three groups of 30 men each. Each group of men is randomly
assigned to a different treatment (placebo, low dose, or high dose). Likewise, the 90 women
are randomly divided into three groups of 30 women each. Each group of women is
randomly assigned to a different treatment (placebo, low dose, or high dose). Is this a
completely randomized design or a randomized block design? Explain your answer.
33)
Use the random number table in Appendix A to obtain the required list of random numbers.
34)
A medical researcher is conducting clinical trials. Of the 60 people participating in the
trial, 20 will receive a placebo, 20 will receive the experimental drug, and 20 will constitute
the control group. The 20 people who will receive the drug will be selected at random.
Construct a list of 20 random numbers between 1 and 60 which can be used in obtaining
the required simple random sample. Use the random number table and use as your
starting point the digits 54 in row 15, columns 20–21.
34)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
35)
35)
A)
Descriptive
B)
Inferential
36)
36)
A)
Simple random sampling
B)
Cluster sampling
C)
Systematic random sampling
D)
Stratified sampling
Answer the question.
37)
37)
A)
The one box that was chosen at random from the 7 boxes
B)
The 7 boxes
C)
The 8 cables chosen randomly for testing
D)
280 cables
Provide an appropriate response.
38)
38)
A)
1
10
B)
2
5
C)
1
5
D)
1
20
A designed experiment is described. Identify the specified element of the experiment.
39)
39)
A)
Method A, method B, method C
B)
Score on reading test
C)
Teaching method and teacher
D)
Juliana, Felix, Sonia, and Helen
Answer the question.
40)
40)
A)
Sample: the 45% of adults who drink at least 48 oz of water; population: all adults
B)
Sample: all adults ; population: the 100,000 selected adults
C)
Sample: the 100,000 selected adults; population: the 45% of adults who drink at least 48 oz of
water
D)
Sample: the 100,000 selected adults; population: all adults
Provide an appropriate response.
41)
41)
A)
Cluster sampling
B)
Stratified sampling
C)
Systematic sampling
D)
Multistage sampling
A designed experiment is described. Identify the specified element of the experiment.
42)
42)
A)
Whether or not (yes or no) the female frogs approached a male dummy
B)
Body type and mating call
C)
Body size, body color, and mating call pitch
D)
Large or small, dark or light, high pitch, normal pitch, or low pitch
C
Provide an appropriate response.
43)
43)
A)
True
B)
False
A
44)
44)
A)
Descriptive
B)
Inferential
A
C
List all possible samples from the specified population.
45)
45)
A)
L,M,B L,M,D L,M,E L,M,J L,B,D L,B,E L,B,J L,D,E L,D,J L,L,M
M,B,D M,B,E M,B,J M,D,E M,D,J M,M,J B,D,E B,B,J B,E,J D,D,J
B)
L,M,B L,M,D L,M,E L,M,J L,B,D L,B,E L,B,J L,D,E L,D,J L,E,J
M,B,D M,B,E M,B,J M,D,E M,D,J M,E,J M,L,B M,L,D M,L,J B,D,E
C)
L,M,B L,M,D L,M,E L,M,J L,B,D L,B,E L,B,J L,D,E L,D,J L,E,J
L,L,M L,L,B L,L,D L,L,E L,L,J M,M,B M,M,D M,M,E M,M,J B,B,D
D)
L,M,B L,M,D L,M,E L,M,J L,B,D L,B,E L,B,J L,D,E L,D,J L,E,J
M,B,D M,B,E M,B,J M,D,E M,D,J M,E,J B,D,E B,D,J B,E,J D,E,J
A designed experiment is described. Identify the specified element of the experiment.
46)
46)
A)
The treatment (i.e., placebo, low dosage of drug, or high dosage of drug)
B)
The participants in the experiment
C)
The three different groups
D)
The diastolic blood pressures of the participants
B
Answer the question.
47)
47)
A)
Sample: all customers; population: the 3 selected customers
B)
Sample: the customers who like chocolate ice cream; population: all customers
C)
Sample: the 3 selected customers; population: the customers who like chocolate ice cream
D)
Sample: the 3 selected customers; population: all customers
D
D
List all possible samples from the specified population.
48)
48)
A)
A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E
B)
A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E B,C,E,A B,D,E,A
C,A,B,D C,E,D,B D,A,C,E
C)
A,B,C,D
D)
A,B,C,D A,B,C,E A,C,D,E A,D,E,B
49)
49)
A)
S,L,P,J S,L,P,M S,L,P,C S,P,J,M S,P,J,C S,P,M,C S,J,M,C L,S,P,J
L,P,J,M L,P,J,C L,P,M,C L,J,M,C P,S,J,M P,J,M,C J,S,M,C
B)
S,L,P,J S,L,P,M S,L,P,C S,L,J,M S,L,J,C S,L,M,C S,J,M,C L,P,J,M
L,S,P,J P,P,J,M L,P,J,C L,P,M,C L,J,M,C P,S,M,C P,J,M,C
C)
S,L,P,J S,L,P,M S,L,P,C S,L,J,M S,L,J,C S,L,M,C S,P,J,M S,P,J,C
S,P,M,C S,J,M,C L,P,J,M L,P,J,C L,P,M,C L,J,M,C P,J,M,C
D)
S,S,L,P S,L,P,J S,L,P,M S,L,P,C S,L,J,M S,P,J,M S,P,J,C S,P,M,C
S,J,M,C L,L,P,J L,P,J,M L,P,J,C L,P,M,C L,J,M,C P,J,M,C
Provide an appropriate response.
50)
50)
A)
Cluster sampling
B)
Stratified sampling
C)
Systematic sampling
D)
Multistage sampling
Answer the question.
51)
51)
A)
The 4 boxes
B)
The 10 cables chosen for testing
C)
200 cables
D)
The one box that was chosen at random from the 4 boxes
Provide an appropriate response.
52)
52)
A)
Stratified sampling
B)
Multistage sampling
C)
Cluster sampling
D)
Systematic sampling
A designed experiment is described. Identify the specified element of the experiment.
53)
53)
A)
The 258 students participating in the study
B)
The three groups of students (those assigned to method A, those assigned to method B, and
those assigned to method C)
C)
Method A, method B, method C
D)
Teaching method and teacher
Provide an appropriate response.
54)
54)
A)
Multistage sampling
B)
Cluster sampling
C)
Stratified sampling
D)
Systematic sampling
A designed experiment is described. Identify the specified element of the experiment.
55)
55)
A)
The dosage of the drug
B)
The participants in the experiment
C)
Diastolic blood pressure
D)
The experimental drug
Provide an appropriate response.
56)
56)
A)
Stratified sampling
B)
Systematic random sampling
C)
Cluster sampling
D)
Simple random sampling
Answer the question.
57)
57)
A)
Sample: the 50,000 selected college students; population: all college students
B)
Sample: the 50,000 selected college students; population: the 74% who answered “yes”
C)
Sample: all college students; population: the 50,000 selected college students
D)
Sample: the 74% who answered “yes”; population: all college students
Provide an appropriate response.
58)
58)
A)
Descriptive
B)
Inferential
Identify the study as an observational study or a designed experiment.
59)
59)
A)
Designed experiment
B)
Observational study
Provide an appropriate response.
60)
60)
A)
Simple random sampling
B)
Cluster sampling
C)
Stratified sampling
D)
Systematic random sampling