BMAL-590 QUANTITATIVE RESEARCH
EXAM QUESTIONS WITH COMPLETE
SOLUTIONS
Probability Trees - Answer-Potential events are represented in a diagram with a branch
for each possible outcome of the events. The probability of each outcome is indicated
on the appropriate branch, and these values can be used to calculate the overall impact
of risk occurrence in a project.
At the ends of the "branches", we calculate joint probabilities as the product of the
individual probabilities on the preceding branches.
The advantage of a probability tree on this type of problem is that it restrains its users
from making the wrong calculation. Once the tree is drawn and the probabilities of the
branches inserted, virtually the only allowable calculation is the multiplication of the
probabilities of linked branches.
Bayes' Law - Answer-𝑃(𝐴│𝐵) = 𝑃(𝐴∩𝐵)/𝑃(𝐵)
The probabilities 𝑃(𝐴) and 𝑃(𝐴𝐶) are called prior probabilities because they are
determined prior to the decision about taking the preparatory course.
The conditional probability 𝑃(𝐴|𝐵)P(A|B) is called a posterior probability (or revised
probability), because the prior probability is revised after the decision about taking the
preparatory course.
Identifying the Correct Method - Answer-Although it is difficult to offer strict rules on
which probability method to use, nevertheless we can provide some general guidelines.
The key issue is whether joint probabilities are provided or are required.
Where the joint probabilities were given, we can compute marginal probabilities by
adding across rows and down columns. We can use the joint and marginal probabilities
to compute conditional probabilities, for which a formula is available. This allows us to
determine whether the events described by the table are independent or dependent. We
can also apply the addition rule to compute the probability that either of two events
occurs.
The first step in assigning probability is to create an exhaustive and mutually exclusive
list of outcomes. The second step is to use the classical, relative frequency, or
subjective approach and assign probability to the outcomes. There are a variety of
methods available to compute the probability of other events. These methods include
,probability rules and trees. An important application of these rules is Bayes' Law, which
allows us to compute conditional probabilities from other forms of probability.
Bayes's Law is used to compute - Answer-posterior probabilities
The classical approach describes a probability - Answer-in terms of the proportion of
times that an event can be theoretically expected to occur
If a set of events includes all the possible outcomes of an experiment, these events are
considered to be - Answer-exhaustive
Which of the following statements is not correct? - Answer-If event A does not occur,
then its complement A' will also not occur.
Sampling Distribution of the Mean - Answer-Sampling distributions describe the
distributions of sample statistics.
There are two ways to create a sampling distribution. The first is to actually draw
samples of the same size from a population, calculate the statistic of interest, and then
use descriptive techniques to learn more about the sampling distribution.
The second method relies on the rules of probablility and the laws of expected value
and variance to derive the sampling distribution.
Central Limit Theorem - Answer-The theory that, as sample size increases, the
distribution of sample means of size n, randomly selected, approaches a normal
distribution.
standard error of the proportion - Answer-the standard deviation of sample proportions,
which measures the average variation around the mean of the sample proportions
The concept that allows us to draw conclusions about the population based strictly on
sample data without having any knowledge about the distribution of the underlying
population is __________ - Answer-the central limit theorem
Each of the following are characteristics of the sampling distribution of the mean except
- Answer-if the original population is not normally distributed, the sampling distribution of
the mean will also be approximately normal for large sample sizes
Each of the following are characteristics of the sampling distribution of the mean: -
Answer-the sampling distribution of the mean has a different mean from the original
population
the standard deviation of the sampling distribution of the mean is referred to as the
standard deviation
, if the original population is not normally distributed, the sampling distribution of the
mean will be normal
Suppose you are given 3 numbers that relate to the number of people in a university
student sample. The three numbers are 10, 20, and 30. If the standard deviation is 10,
the standard error equals - Answer-5.77
You are tasked with finding the sample standard deviation. You are given 4 numbers.
The numbers are 5, 10, 15, and 20. The sample standard deviation equals - Answer-
6.455
Two methods exist to create a sampling distribution. One involves using parallel
samples from a population and the other is to use the - Answer-rules of probability
hypothesis testing - Answer-make and test an educated guess about a problem/solution
null hypothesis - Answer-a statement or idea that can be falsified, or proved wrong
represented by 𝐻0 (pronounced H-nought)
alternative or research hypothesis - Answer-the opposite of null hypothesis- consists of
a statement about the expected relationship between the variables
denoted 𝐻1
Type I Error - Answer-occurs when we reject a true null hypothesis.
denoted by 𝛼, which is also called the significance level
Type II Error - Answer-defined as not rejecting a false null hypothesis
denoted by 𝛽 (Greek letter beta)
The error probabilities 𝛼 and 𝛽 are inversely related, meaning that any attempt to
reduce one will increase the other.
Critical Concepts in Hypothesis Testing - Answer-1. There are two hypotheses. One is
called the null hypothesis and the other the alternative or research hypothesis.
2. The testing procedure begins with the assumption that the null hypothesis is true.
3. The goal of the process is to determine whether there is enough evidence to infer that
the alternative hypothesis is true.
EXAM QUESTIONS WITH COMPLETE
SOLUTIONS
Probability Trees - Answer-Potential events are represented in a diagram with a branch
for each possible outcome of the events. The probability of each outcome is indicated
on the appropriate branch, and these values can be used to calculate the overall impact
of risk occurrence in a project.
At the ends of the "branches", we calculate joint probabilities as the product of the
individual probabilities on the preceding branches.
The advantage of a probability tree on this type of problem is that it restrains its users
from making the wrong calculation. Once the tree is drawn and the probabilities of the
branches inserted, virtually the only allowable calculation is the multiplication of the
probabilities of linked branches.
Bayes' Law - Answer-𝑃(𝐴│𝐵) = 𝑃(𝐴∩𝐵)/𝑃(𝐵)
The probabilities 𝑃(𝐴) and 𝑃(𝐴𝐶) are called prior probabilities because they are
determined prior to the decision about taking the preparatory course.
The conditional probability 𝑃(𝐴|𝐵)P(A|B) is called a posterior probability (or revised
probability), because the prior probability is revised after the decision about taking the
preparatory course.
Identifying the Correct Method - Answer-Although it is difficult to offer strict rules on
which probability method to use, nevertheless we can provide some general guidelines.
The key issue is whether joint probabilities are provided or are required.
Where the joint probabilities were given, we can compute marginal probabilities by
adding across rows and down columns. We can use the joint and marginal probabilities
to compute conditional probabilities, for which a formula is available. This allows us to
determine whether the events described by the table are independent or dependent. We
can also apply the addition rule to compute the probability that either of two events
occurs.
The first step in assigning probability is to create an exhaustive and mutually exclusive
list of outcomes. The second step is to use the classical, relative frequency, or
subjective approach and assign probability to the outcomes. There are a variety of
methods available to compute the probability of other events. These methods include
,probability rules and trees. An important application of these rules is Bayes' Law, which
allows us to compute conditional probabilities from other forms of probability.
Bayes's Law is used to compute - Answer-posterior probabilities
The classical approach describes a probability - Answer-in terms of the proportion of
times that an event can be theoretically expected to occur
If a set of events includes all the possible outcomes of an experiment, these events are
considered to be - Answer-exhaustive
Which of the following statements is not correct? - Answer-If event A does not occur,
then its complement A' will also not occur.
Sampling Distribution of the Mean - Answer-Sampling distributions describe the
distributions of sample statistics.
There are two ways to create a sampling distribution. The first is to actually draw
samples of the same size from a population, calculate the statistic of interest, and then
use descriptive techniques to learn more about the sampling distribution.
The second method relies on the rules of probablility and the laws of expected value
and variance to derive the sampling distribution.
Central Limit Theorem - Answer-The theory that, as sample size increases, the
distribution of sample means of size n, randomly selected, approaches a normal
distribution.
standard error of the proportion - Answer-the standard deviation of sample proportions,
which measures the average variation around the mean of the sample proportions
The concept that allows us to draw conclusions about the population based strictly on
sample data without having any knowledge about the distribution of the underlying
population is __________ - Answer-the central limit theorem
Each of the following are characteristics of the sampling distribution of the mean except
- Answer-if the original population is not normally distributed, the sampling distribution of
the mean will also be approximately normal for large sample sizes
Each of the following are characteristics of the sampling distribution of the mean: -
Answer-the sampling distribution of the mean has a different mean from the original
population
the standard deviation of the sampling distribution of the mean is referred to as the
standard deviation
, if the original population is not normally distributed, the sampling distribution of the
mean will be normal
Suppose you are given 3 numbers that relate to the number of people in a university
student sample. The three numbers are 10, 20, and 30. If the standard deviation is 10,
the standard error equals - Answer-5.77
You are tasked with finding the sample standard deviation. You are given 4 numbers.
The numbers are 5, 10, 15, and 20. The sample standard deviation equals - Answer-
6.455
Two methods exist to create a sampling distribution. One involves using parallel
samples from a population and the other is to use the - Answer-rules of probability
hypothesis testing - Answer-make and test an educated guess about a problem/solution
null hypothesis - Answer-a statement or idea that can be falsified, or proved wrong
represented by 𝐻0 (pronounced H-nought)
alternative or research hypothesis - Answer-the opposite of null hypothesis- consists of
a statement about the expected relationship between the variables
denoted 𝐻1
Type I Error - Answer-occurs when we reject a true null hypothesis.
denoted by 𝛼, which is also called the significance level
Type II Error - Answer-defined as not rejecting a false null hypothesis
denoted by 𝛽 (Greek letter beta)
The error probabilities 𝛼 and 𝛽 are inversely related, meaning that any attempt to
reduce one will increase the other.
Critical Concepts in Hypothesis Testing - Answer-1. There are two hypotheses. One is
called the null hypothesis and the other the alternative or research hypothesis.
2. The testing procedure begins with the assumption that the null hypothesis is true.
3. The goal of the process is to determine whether there is enough evidence to infer that
the alternative hypothesis is true.
