REM B LVL 2

Question 1

1+0i is ___ for complex number z.

A. additive identity element
B. multiplicative identity element
C. multiplicative inverse

Answer 1

B. multiplicative identity element

On multiplying one (1+0i) to a complex number, we get same complex number so 1+0i is multiplicative identity element for complex number z i.e. z*1=z.

Question 2

1/z is ____ for complex number z

A. multiplicative identity element
B. multiplicative inverse
C. additive identity element
D. additive inverse

Answer 2

B. multiplicative inverse

On multiplying reciprocal of complex
number (1/z) to complex number z, we
get multiplying inverse one i.e. z*1=z.

Question 3

O+0i is ___ for complex number z.

A. multiplicative inverse
B. additive inverse
C. additive identity element
D. additive inverse

Answer 3

C. additive identity element

On adding zero (0+0i) to a complex
number, we get same complex number so 0+0i is additive identity element for complex number z i.e. z+0 = z.

Question 4

-z is ___ for complex number z.

A. additive identity element
B. multiplicative inverse
C. additive identity element
D. additive inverse

Answer 4

D. additive inverse

On adding negative of complex number
(-z) to complex number z, we get
additive identity element zero i.e. z+(-z)=0.

Question 5

The sequence a_n = 5n is ___

A. convergent
B. properly divergent
C. oscillating
D. bounded

Answer 5

B. properly divergent

As n approaches oo, the value of an also approaches 00. Thus, this is a properly divergent sequence.

Question 6

A partial differential equation has

A. equal number of dependent and
independent variables
B. more than one dependent variable
C. two or more independent variables

Answer 6

C. two or more independent variables

A partial differential equation has more
than one independent variables. An
ordinary differential equation has only
one independent variable.

Question 7

2x(d^4 y/dx^4) + sx^2 (dy/dx)^(1/2)-
xy=O

A. 4th order, 2nd degree
B. 4th order, 1/2 degree
C. 2nd order, 4th degree
D. 4th order, 1st degree

Answer 7

A. 4th order, 2nd degree

Question 8

Why is data cleaning important in the
analysis process?

A. It helps establish the questions to be
answered.
B. It allows for the extraction of relevant
insights.
C. It ensures data accuracy and reliability.
D. It supports decision-making based on
evidence.

Answer 8

C. It ensures data accuracy and reliability.

Data cleaning is important as it ensures
data accuracy and reliability for
analysis. By removing duplicates, fixing
formatting errors, and eliminating
irrelevant or incomplete responses, the
analysis can be conducted with
confidence in the data quality.

Question 9

What is the purpose of a data
management platform (DMP)?

A. To manipulate and segment data for
analysis
B. To define the objective of the data analysis
C. To collect and aggregate data from
numerous sources

Answer 9

C. To collect and aggregate data from
numerous sources

A data management platform (DMP) is
a software tool that allows the
identification and aggregation of data
from various sources. It helps in
collecting and organizing the data
before further manipulation,
segmentation, and analysis.

Question 10

are used when we want to visually examine the relationship between two quantitative variables.

A. Bar graph
B. Scatterplot
C. Pie chart

Answer 10

B. Scatterplot

Dots are used to indicate values for two different numeric variables in a scatter plot, also known as a scatter chart or a scatter graph. The values for each data point are indicated by the position of
each dot on the horizontal and vertical axes. Scatter plots are used to see how variables relate to one another.

Question 11

Which type of interval estimation is used to estimate the proportion of nonconforming items in a sample?

A. Coverage interval
B. Prediction interval
C. Tolerance interval
D. Confidence interval

Answer 11

C. Tolerance interval

Tolerance intervals are used to estimate the proportion of nonconforming items or the percentage of items within
certain limits. Tolerance intervals bound
the range of values which is likely to
contain a certain proportion of a
population, and their width is
determined not only by sampling error,
but also variance in the population
itself.

Question 12

Which of the following conditions must
hold true for a Poisson random
variable?

A. The number of successes in two disjoint
time intervals is dependent.
B. The probability of success during a
given small time interval is proportional
to the length of the time interval.
C. The probability of success during a given
small time interval is constant.

Answer 12

B. The probability of success during a
given small time interval is proportional
to the length of the time interval.

The Poisson random variable follows the condition that the probability of success during a given small time interval is proportional to the entire length of the time interval.

Question 13

In a Poisson Distribution, the mean and
variance are equal.

A. False
B. Partly true
C. Partly false
D. True

Answer 13

D. True

The mean and the variance of the
Poisson distribution are both equal to μ.
Remember that, in a Poisson
distribution, only one parameter, μ is
needed to determine the probability of
any given event.

Question 14

Which of the following is/are examples
of discrete random variable/s?
1. To determine the number of houses
in a certain block.
2. Getting the number of fish caught in
a pond.
3. Measuring the height of a person.
4. Tossing two coins.

A. 1,2 and 3
B. 1,2,and 4
C. 1,2,3 and 4
D. 2 and 4

Answer 14

B. 1,2,and 4

A random variable is a variable whose
value is a numerical outcome of a
random phenomenon.

There are two types of a random
variable

Discrete Random Variable which can be
obtained by counting (Nos. 1,2 and 4)

Continuous Random Variable which can
be obtained by measuring (No.3-
Measuring the height of a person is
continuous)

Question 15

Which statistical test is commonly used
to compare means between two
independent groups?

A. Mann-Whitney U test
B. Independent samples t-test
C. Paired t-test

Answer 15

B. Independent samples t-test

A t test is a statistical test that is used to compare the means of two groups.It is often used in hypothesis testing to
determine whether a process or
treatment actually has an effect on the population of interest, or whether two groups are different from one another.

Question 16

The distribution that is formed by all
possible values of a statistics is known as

A. Binomial distribution
B. Sampling distribution
C. Normal distribution
D. Hypergeometric distribution

Answer 16

B. Sampling distribution

The sampling distribution of a statistic is the distribution of all possible values taken by the statistic when all possible samples of a fixed size n are taken from the population.

Question 17

What is the purpose of a confidence
interval in engineering data analysis?

A. To provide a range of values within
which the population mean is likely to
fall
B. To determine the sample mean accurately
C. To minimize the variability of the data

Answer 17

A. To provide a range of values within
which the population mean is likely to
fall

A confidence interval shows the
probability that a parameter will fall between a pair of values around the mean. Confidence intervals show the degree of uncertainty or certainty in a sampling method.

Question 18

Which of the following is an application
of the Poisson distribution?

A. Predicting the stock market prices
B. Estimating the average salary of
employees
C. Modeling the number of typing errors
found on a page in a book.

Answer 18

C. Modeling the number of typing errors
found on a page in a book.

The Poisson distribution is commonly
used to model the number of discrete
events that occur within a fixed interval
of time or space. In this case, we are
considering the number of typing errors found on a page in a book. Typing errors can be considered as discrete events
that can occur randomly.

Question 19

Which distribution is suitable for modeling waiting times between events?

A. Poisson distribution
B. Exponential distribution
C. Binomial distribution
D. Uniform distribution

Answer 19

B. Exponential distribution

Exponential distribution is commonly
used for modeling waiting times
between events, such as the time
between customer arrivals.

Question 20

What is the main difference between a
confidence interval and a prediction
interval?

A. Confidence intervals are narrower than
prediction intervals.
B. Confidence intervals estimate means,
while prediction intervals estimate
variances.
C. Confidence intervals estimate
population parameters, while prediction
intervals estimate sample statistics.

Answer 20

C. Confidence intervals estimate
population parameters, while prediction
intervals estimate sample statistics.

The prediction interval predicts in what range a future individual observation will fall, while a confidence interval shows
the likely range of values associated with some statistical parameter of the data, such as the population mean.

Question 21

Which of the following is not correct
about quota sampling?

A. It is objective
B. It is based on the experience of researcher
C. It is subjective

Answer 21

A. It is objective

Sampling is a research technique used for selecting individual members or a subset of the population to make
statistical inferences from them and
estimate the characteristics of the
whole population. The population
includes all members from a specified
group and all possible outcomes or
measurements of interest. Quota
sampling is a sampling methodology
wherein data is collected from a
homogeneous (same characteristics)
group. It involves a two-step process
where two variables can be used to filter
information from the population. It
comes under the non-probability sampling method. It is based on subjective analysis. Thus, quota sampling is not objective.

Question 22

In a two-sample hypothesis testing
problem, what is the focus of the
hypothesis?

A. Testing the hypothesis about the
difference between the sample mean and
a known value.
B. Testing the hypothesis about the
difference between the sample mean and
a predicted value.
C. Testing the hypothesis about the
difference between two population
means.

Answer 22

C. Testing the hypothesis about the
difference between two population
means.

In a two-sample hypothesis testing
problem, the focus of the hypothesis is
to determine if there is a significant
difference between the means of two
populations.

Question 23

The power of a statistical test is

A. The probability of making a Type I error
B. The ability to detect an effect or
difference when it exists
C. The probability of making a Type Il error

Answer 23

B. The ability to detect an effect or
difference when it exists

The power of a statistical test is the
probability that it will correctly lead to the rejection of a null hypothesis (HO)when it is false- i.e. the ability of the test to detect an effect, if the effect actually exists. Statistical power is inversely related to beta or the
probability of making a type Il error.

Question 24

Choose the correct option for the
regression line passing through the
origin.

A. Association is zero
B. The regression coefficient is zero
C. Intercept is zero

Answer 24

C. Intercept is zero

When the regression line passes
through the origin, it means that the
intercept of the regression equation is
zero. The intercept represents the
predicted value of the dependent
variable when the independent
variable(s) is zero. In this case, since the regression line passes through the origin, the predicted value of the
dependent variable is zero when the
independent variable(s) is zero. It is
important to note that a regression line
passing through the origin does not
necessarily indicate that the correlation,regression coefficient, or association is zero. The correlation and association
between the variables can still be
present, and the regression
coefficient(s) for the independent
variable(s) other than the intercept can
have non-zero values

Question 25

Choose the correct example for positive
correlation.

A. Weight and income
B. Income and expenditure
C. Price and demand

Answer 25

B. Income and expenditure

Question 26

How many coefficients do you need to estimate in a simple linear regression model (One independent variable)?

A. 2
B. 1
C. 4
D. -1

Answer 26

A. 2

Question 27

If one regression coefficient is greater
than one, then other will be

A. Equal to minus one
B. Equal to one
C. Less than one

Answer 27

C. Less than one

Regression coefficients are independent
of change of origin but not of scale. If
one regression coefficient is greater than unit, then the other must be less than unit but not vice versa.

Question 28

The independent variable is used to
explain the dependent variable in

A. None of these choices
B. Linear regression analysis
C. Multiple regression analysis

Answer 28

B. Linear regression analysis

In linear regression analysis, the
relationship between the independent variable(s) and the dependent variable is modeled using a linear equation.

The independent variable(s) are used as
predictors or explanatory variables to estimate the values of the dependent variable.

Multiple regression analysis is a specific
type of linear regression analysis that
involves multiple independent variables

Non-linear regression analysis involves modeling the relationship between
variables using non-linear equations or
models.

Question 29

To determine the height of a person
when his weight is given is a/an

A. Association problem
B. Anova problem
C. Regression problem
D Correlation problem

Answer 29

C. Regression problem

Question 30

Graeco-Latin design allows for ___ blocking factors.

A. Three
B. Five
C. Two
D. One

Answer 30

A. Three

Graeco-Latin is simply two
superimposed Latin Square design with
one using the Latin Letters and the
other using the Greek letters, resulting in
a design with four factors. Therefore,
the error can be controlled in three
directions by blocking three nuisance
factors.

Question 31

What does a two-level factorial
experiment involve?

A. Testing each factor at three different
levels.
B. Testing each factor at the highest and
lowest levels
C. Testing each factor at random levels.

Answer 31

B. Testing each factor at the highest and
lowest levels

A two-level factorial experiment involves
testing each factor at the highest and
lowest levels, typically denoted as +1
and -1, respectively.

Question 32

What is the purpose of statistical
hypothesis testing in experimental data
analysis?

A. To determine the statistical
significance of observed differences.
B. To compare mean values of different
variables.
C. To gather historical data for analysis.

Answer 32

A. To determine the statistical
significance of observed differences.

Statistical hypothesis testing is used to
assess the statistical significance of
observed differences, such as
comparing means or investigating the
effects of variables.

Question 33

What is the purpose of statistical
hypothesis testing in experimental data
analysis?

A. To determine the statistical
significance of observed differences.
B. To compare mean values of different
variables.
C. To gather historical data for analysis.

Answer 33

A. To determine the statistical
significance of observed differences.

Statistical hypothesis testing is used to
assess the statistical significance of
observed differences, such as
comparing means or investigating the
effects of variables.

Question 34

Point out the wrong statement.

A. Causal relationships may not apply to
every individual
B. Complication approached exist for
inferring causation
C All of these choices
D. Randomized studies are not used to
identify causation

Answer 34

D. Randomized studies are not used to
identify causation

Randomized studies, particularly
randomized controlled trials (RCTs), are
widely recognized as one of the most
rigorous and reliable methods for
establishing causal relationships. By
randomly assigning participants to
different groups or interventions,
researchers can minimize bias and
confounding factors, allowing them to
make causal inferences. Randomization
helps ensure that any observed
differences in outcomes between
groups are more likely to be due to the intervention being studied rather than other factors.

Question 35

Which of these does not come into the
general model of a process?

A. Acceptance sampling
B. Input
C. Controllable input factors
D. Uncontrollable inputs factors

Answer 35

A. Acceptance sampling

The general model of process describes a process to which the input is provided in the presence of controllable factors
and uncontrollable input factors, to get
an output.

Question 36

Which of the following is NOT a role of
statistical methods in engineering
experiments?

A. Replacing the need for conducting
experiments.
B. Analyzing the data collected from the
experiment.
C. Planning the experiment design.

Answer 36

A. Replacing the need for conducting
experiments.

Statistical methods complement the
experimental process but do not replace
the need for conducting experiments.

Question 37

What role do statistical thinking and
statistical methods play in engineering
experiments?

A. They eliminate the need for conducting
experiments.
B. They are only used in manufacturing
processes, not design and development.
C. They provide important insights into
the experimental design.
D. They are irrelevant and not used in
engineering experiments

Answer 37

C. They provide important insights into
the experimental design.

Statistical thinking and statistical
methods are essential in planning,
conducting, and analyzing the data from
engineering experiments, providing
valuable insights into the experimental
design.

Question 38

What is the main advantage of using
fractional factorial designs in DOE?

A. Enhanced ability to analyze interactions
between factors
B. Elimination of the need for replication
C. Increased precision in estimating factor
effects
D. Reduction in the number of
experimental runs required

Answer 38

D. Reduction in the number of
experimental runs required

Fractional factorial designs allow for
investigating only a portion of the
possible combinations, reducing the number of experimental runs required compared to a full factorial design.