BMAL-590 Quantitative Research Questions With Solutions
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Course
BMAL 590
Institution
BMAL 590
BMAL-590 Quantitative Research Questions
With Solutions
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 pea...
BMAL-590 Quantitative Research Questions
With Solutions
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
, BMAL-590 Quantitative Research Questions
With Solutions
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.
, BMAL-590 Quantitative Research Questions
With Solutions
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!
, BMAL-590 Quantitative Research Questions
With Solutions
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% (19/20 = 0.95), while our significance level is 5%. A 5% significance level means, that in
the long run, this type of conclusion will be wrong 5% of the time.
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