BMAL-590 QUANTITATIVE RESEARCH EXAM QUESTIONS AND
ANSWERS WITH COMPLETE SOLUTIONS LATEST UPDATE
What Is Statistics?
"Statistics is a way to get information from data."
Statistics is a tool for creating new understanding from a set of numbers.
You need data and information
descriptive statistics
one of two branches of statistics which focuses on methods of organizing, summarizing, and presenting
data in a convenient and informative way.
One form of descriptive statistics uses graphical techniques which allow statistics practitioners to present
data in ways that make it easy for the reader to extract useful information.
Another form of descriptive statistics uses numerical techniques to summarize data. Rather than
providing the raw data, the professor may only share summary data with the student.
Histogram
(or bar graph) can show if the data is evenly distributed across the range of values, if it falls
symmetrically from a center peak (normal distribution), if there is a peak but the more of the data falls
,on one side of the peak than the other (a skewed distribution), or if there are two or more peaks in the
data (bi- or multi-modal).
average
mean
range
calculated by subtracting the smallest number from the largest.
mode
the most frequently occurring score(s) in a distribution
variance
the average squared deviation from the mean
Standard deviation
the square root of the variance and gets the variability measure back to the same units as the data.
Standard deviation has many useful properties when the data is normally distributed
inferential statistics
a body of methods used to draw conclusions or inferences about characteristics of populations based on
sample data.
Exit polls are a very common application of statistical inference.
Statistical inference problems involve three key concepts:
population, the sample, and the statistical inference.
,Population:
the group of all items of interest to a statistics practitioner. It is frequently very large and may, in fact, be
infinitely large. In the language of statistics, population does not necessarily refer to a group of people. It
may, for example, refer to the population of diameters of ball bearings produced at a large plant.
A descriptive measure of a population is called a parameter. In most applications of inferential statistics,
the parameter represents the information we need.
Sample
a set of data drawn from the population. A descriptive measure of a sample is called a statistic. We use
statistics to make inferences about parameters.
statistical inference
the process of making an estimate, prediction, or decision about a population based on sample data.
Because populations are almost always very large, investigating each member of the population would
be impractical and expensive. It is far easier and cheaper to take a sample from the population of
interest and draw conclusions or make estimates about the population on the basis of information
provided by the sample. However, such conclusions and estimates are not always going to be correct. For
this reason, we build into the statistical inference a measure of reliability.
There are two such measures, the confidence level and the significance level. The confidence level is the
proportion of times that an estimating procedure will be correct. When the purpose of the statistical
inference is to draw a conclusion about a population, the significance level measures how frequently the
conclusion will be wrong in the long run.
, Statistical inference is the process of making an estimate, prediction, or decision about a population
based on a sample.
What can we infer about a Population's Parameters based on a Sample's Statistics?
Since statistical inference involves using statistics to make inferences about parameters, we can make an
estimate, prediction, or decision about a population based on sample data. We can apply what we know
about a sample to the larger population from which it was drawn!
Confidence level
the proportion of times that an estimating procedure will be correct. A confidence level of 95% means
that estimates based on this form of statistical inference will be correct 95% of the time.
significance level
measures how frequently the conclusion will be wrong in the long run. A 5% significance level means
that, in the long run, this type of conclusion will be wrong 5% of the time.
𝛼
Greek letter "alpha"
If we use 𝛼 to represent significance, then our confidence level is 1−𝛼
Confidence Level + Significance Level = 1
Consider a statement from polling data you may hear about in the news: "This poll is considered
accurate within 3.4 percentage points, 19 times out of 20." In this case, our confidence level is 95%
ANSWERS WITH COMPLETE SOLUTIONS LATEST UPDATE
What Is Statistics?
"Statistics is a way to get information from data."
Statistics is a tool for creating new understanding from a set of numbers.
You need data and information
descriptive statistics
one of two branches of statistics which focuses on methods of organizing, summarizing, and presenting
data in a convenient and informative way.
One form of descriptive statistics uses graphical techniques which allow statistics practitioners to present
data in ways that make it easy for the reader to extract useful information.
Another form of descriptive statistics uses numerical techniques to summarize data. Rather than
providing the raw data, the professor may only share summary data with the student.
Histogram
(or bar graph) can show if the data is evenly distributed across the range of values, if it falls
symmetrically from a center peak (normal distribution), if there is a peak but the more of the data falls
,on one side of the peak than the other (a skewed distribution), or if there are two or more peaks in the
data (bi- or multi-modal).
average
mean
range
calculated by subtracting the smallest number from the largest.
mode
the most frequently occurring score(s) in a distribution
variance
the average squared deviation from the mean
Standard deviation
the square root of the variance and gets the variability measure back to the same units as the data.
Standard deviation has many useful properties when the data is normally distributed
inferential statistics
a body of methods used to draw conclusions or inferences about characteristics of populations based on
sample data.
Exit polls are a very common application of statistical inference.
Statistical inference problems involve three key concepts:
population, the sample, and the statistical inference.
,Population:
the group of all items of interest to a statistics practitioner. It is frequently very large and may, in fact, be
infinitely large. In the language of statistics, population does not necessarily refer to a group of people. It
may, for example, refer to the population of diameters of ball bearings produced at a large plant.
A descriptive measure of a population is called a parameter. In most applications of inferential statistics,
the parameter represents the information we need.
Sample
a set of data drawn from the population. A descriptive measure of a sample is called a statistic. We use
statistics to make inferences about parameters.
statistical inference
the process of making an estimate, prediction, or decision about a population based on sample data.
Because populations are almost always very large, investigating each member of the population would
be impractical and expensive. It is far easier and cheaper to take a sample from the population of
interest and draw conclusions or make estimates about the population on the basis of information
provided by the sample. However, such conclusions and estimates are not always going to be correct. For
this reason, we build into the statistical inference a measure of reliability.
There are two such measures, the confidence level and the significance level. The confidence level is the
proportion of times that an estimating procedure will be correct. When the purpose of the statistical
inference is to draw a conclusion about a population, the significance level measures how frequently the
conclusion will be wrong in the long run.
, Statistical inference is the process of making an estimate, prediction, or decision about a population
based on a sample.
What can we infer about a Population's Parameters based on a Sample's Statistics?
Since statistical inference involves using statistics to make inferences about parameters, we can make an
estimate, prediction, or decision about a population based on sample data. We can apply what we know
about a sample to the larger population from which it was drawn!
Confidence level
the proportion of times that an estimating procedure will be correct. A confidence level of 95% means
that estimates based on this form of statistical inference will be correct 95% of the time.
significance level
measures how frequently the conclusion will be wrong in the long run. A 5% significance level means
that, in the long run, this type of conclusion will be wrong 5% of the time.
𝛼
Greek letter "alpha"
If we use 𝛼 to represent significance, then our confidence level is 1−𝛼
Confidence Level + Significance Level = 1
Consider a statement from polling data you may hear about in the news: "This poll is considered
accurate within 3.4 percentage points, 19 times out of 20." In this case, our confidence level is 95%
