REM B LVL 3

Question 1

An ODE of form M(x,y)dx +N(x,y)dy=0
is

A. Exact
B. Nonlinear
C. Particular

Answer 1

A. Exact

Question 2

A d^2 u/dx^2+B d^2 u/dxdy+C d^2 u/
dy^2+D=0,if B^2-4AC=0 it is?

A. Elliptic.
B. Hyperbolic.
C. Toroid
D. Parabolic.

Answer 2

A. Elliptic.

Question 3

What is the purpose of transcribing
interviews in engineering data analysis?

A. To categorize and organize the data
through coding
B. To compare and contrast participant
responses
C. To determine the sample size for
statistical analysis

Answer 3

A. To categorize and organize the data
through coding

Transcribing interviews involves
converting recorded interviews into
written format. Transcriptions facilitate
in-depth analysis and coding of the
data, helping categorize and organize
the information efficiently.

Question 4

What are the hazards associated with
using historical data for analysis?

A. Potential transcription or recording
errors.
B. Lack of statistical analysis techniques
C. Difficulty in identifying relevant variables.

Answer 4

A. Potential transcription or recording
errors.

Using historical data for analysis can introduce transcription or recording errors, which may lead to outliers or unusual values that can affect the
results.

Question 5

Which type of analysis helps companies
decide on new products or areas of
business to invest in?

A. Prescriptive analysis
B. Diagnostic analysis
C. Predictive analysis

Answer 5

A. Prescriptive analysis

Prescriptive analysis helps in making
recommendations for the future,
including decisions on new products or
areas of investment.

Question 6

Given below are two statements
Statement I: Like the normal
distribution, the t-distribution has a
smooth shape.
Statement II: As the sample size
decreases, the t-distribution becomes
more similar to a normal distribution.
In light of the above statements, choose the most appropriate answer from the options given below

A. Both Statement I and Statement II are
incorrect
B. Statement I is incorrect but Statement Il is
correct
C. Statement I is correct but Statement l
is incorrect

Answer 6

C. Statement I is correct but Statement l
is incorrect

Question 7

Which of the example requires snowball
sampling technique?

A. Students with hearing impairments
B. Non-heterosexual persons
C. First generation learners

Answer 7

B. Non-heterosexual persons

Question 8

In a one-tail test for the population
mean, if the null hypothesis is not
rejected when the alternative hypothesis
is true, then

A. A Type II Error Is Committed
B. A Type I Error Is Committed
C. A Two-Tail Test Should Be Used Instead of
a One-Tail Test

Answer 8

A. A Type II Error Is Committed

Question 9

When the p-value is less than the level
of significance (a), what decision is
made?

A. Conduct additional analysis
B. Fail to reject the null hypothesis
C. Reject the null hypothesis

Answer 9

C. Reject the null hypothesis

If a p-value is lower than our
significance level, we reject the null
hypothesis. If not, we fail to reject the
null hypothesis.

Question 10

If “time” is used as the independent variable in a simple linear regression analysis, then which of the following assumption could be violated?

A. The residual variation is the same for all
fitted values of Y
B. There is a linear relationship between the
independent and dependent variables
C. Successive observations of the
dependent variable are uncorrelated

Answer 10

C. Successive observations of the
dependent variable are uncorrelated

Question 11

When the error terms have a constant variance, a plot of the residuals versus the independent variable x that

A. fans out, but then funnels in
B. fans out
C. forms a horizontal band pattern

Answer 11

B. fans out

Question 12

Which one of the following statements
about the correlation coefficient is
correct?

A. Both the change of scale and the change of origin have no effect on the correlation coefficient.
B. The correlation coefficient is unaffected by
scale changes.
C. The correlation coefficient is
unaffected by the change of origin.

Answer 12

C. The correlation coefficient is
unaffected by the change of origin.

Question 13

What is the purpose of randomization in
experimental design?

A. To assign factors randomly to treatment
groups.
B. To ensure that every possible combination
of factor levels is tested.
C. To eliminate any variability in the
experimental results.
D. To reduce bias and prevent systematic
errors.

Answer 13

D. To reduce bias and prevent systematic
errors.

Question 14

Which of the following are important in
designing an experiment?
I. Control of all variables that might have
an influence on the response variable.
II. Randomization of subjects to
treatment groups.
III. Use a large number of subjects to
control for small-sample variability.

A. I and Il only
B. II and Ill only
C. I, Il, and IIl

Answer 14

C. I, Il, and IIl

Question 15

The lowest design resolution in which
main effects are not confounded with 2-
way interactions is called

A. Resolution V design
B. Resolution VI design
C. Resolution IV design
D. Resolution III design

Answer 15

C. Resolution IV design

Resolution Ill designs - These are
designs in which no main effects are
aliased with any other main effect, but
main effects aliased with two-factor
interactions and two-factor interactions
may be aliased with each other.

Resolution IV designs - These are
designs in which no main effect is
aliased with any other main effect or
with any two-factor interaction, but two-
factor interactions are aliased with
other

Resolution V designs -These are
designs in which no main effect or two-
factor interaction is aliased with any
other main effect or two-factor
interaction, but two-factor interactions
are aliased with three-factor
interactions.

Question 16

What does a factorial experiment allow
for in studying complex systems?

A. The use of historical data instead of
experimentation.
B. The elimination of statistical thinking and
methods.
C. The manipulation of multiple factors
simultaneously.

Answer 16

C. The manipulation of multiple factors
simultaneously.

Factorial experiments allow for the
manipulation of multiple factors
simultaneously, enabling the study of
their combined effects on complex
systems.

Question 17

What is the purpose of analyzing data
from a designed experiment?

A. To establish cause-and-effect
relationships.
B. To confirm the applicability of scientific
theories.
C. To compare mean values without
statistical analysis.

Answer 17

A. To establish cause-and-effect
relationships.

The purpose of analyzing data from a
designed experiment is to identify and
establish cause-and-effect relationships between the controllable variables and the observed changes in output
performance.

Question 18

A double-blind design is important in an
experiment because

A. Subjects in a study might react differently if they knew they were receiving an active treatment or a placebo.
B. There is a natural tendency for subjects in
an experiment to want to please the
researcher.
C. All of the above are reasons why an
experiment should be double-blind.

Answer 18

C. All of the above are reasons why an
experiment should be double-blind.

Question 19

If the effects of two treatment
combinations are confounded, then one
effect is said to be the ___ of the other.

A. Alias
B. Reciprocal
C. Co-treatment

Answer 19

A. Alias

When two effects in an experimental
design are confounded, it means that
their influences cannot be distinguished
or separated from each other. In other
words, the observed outcome or
response variable cannot be attributed
solely to one specific treatment or
factor because the effects of the two treatments are intertwined or mixed together. In this context, one effect is said to be the “alias” of the other. It
implies that the two effects are
indistinguishable or inseparable, and it
is not possible to determine the
individual contribution or impact of each
treatment on the observed outcome.

The aliasing of effects is a common
issue in experimental design, and it can
lead to challenges in interpreting the
results accurately.

Question 20

The lowest design resolution in which main effects are not confounded with any other main effect is called

A. Resolution V design
B. Resolution III design
C. Resolution VI design

Answer 20

B. Resolution III design

Resolution III designs - These are
designs in which no main effects are aliased with any other main effect, but main effects aliased with two-factor
interactions and two-factor interactions
may be aliased with each other.

Resolution IV designs - These are
designs in which no main effect is
aliased with any other main effect or
with any two-factor interaction, but two-
factor interactions are aliased with
other

Resolution V designs -These are
designs in which no main effect or two-
factor interaction is aliased with any
other main effect or two-factor
interaction, but two-factor interactions
are aliased with three-factor
interactions.

Question 21

How does blocking differ from
randomization in experimental design?

A. Blocking reduces the need for replication,while randomization increases statistical power.
B. Blocking restricts randomization, while
randomization ensures equal
representation.
C. Blocking controls for known factors, while
randomization controls for unknown
factors.
D. Blocking ensures a balanced distribution,
while randomization eliminates
confounding effects.

Answer 21

B. Blocking restricts randomization, while
randomization ensures equal
representation.

Blocking restricts randomization by
carrying out all trials with one setting of
a factor before switching, while
randomization ensures an equal representation of factor levels by randomizing the order of trials.

Question 22

Which of these steps are not conducted
when the design of experiment
procedure is adopted?

A. Determining where to set the influential
controllable inputs so that the variability in
the output is smallest
B. Determining which variable is most
influential to output
C. Deleting the uncontrollable factors

Answer 22

C. Deleting the uncontrollable factors

When the design of experiment (DOE)
procedure is adopted, the steps typically
involve determining the influential
variables, setting the influential
controllable factors, and optimizing the controllable inputs. However, deleting uncontrollable factors is not a step in the DOE procedure. Uncontrollable
factors are not within the control of the experimenter, so they cannot be deleted or removed from the experiment.