11. You do a survey of business students and liberal arts school students to
find out how many times a week they read a daily newspaper. In each group, you
interview 100 students. You find the following: Xb=4.5 times per week, Sb=1.5,
Xia=5.6 times per week, Sia=2.0. Test the hypothesis that there is no significant
difference between these two samples.
The process of deciding whether or not two sets of data is statistically different in
a significant way starts if two or more sets occur in a population. For a data set to be
statistically significant, the researcher must be able to accurately calculate a large enough
observed difference that the chance of this occurring in a random sampling is miniscule
(Schindler, 2019, p. 392). Put another way, with a larger sample base, this projects a
guaranteed statistical significance and results in a practical application when size brings
more results (Khalilzadeh & Tasci, 2017, para. 1). Additionally, Schindler (2019) clearly
states, “In selecting a significance test, one needs to know, at a minimum, the number of
samples, their independence or relatedness, and the measurement level of the data” (p.
392).
From the beginning, the number provided of number samples in each test group
for the interview is 100. The common thread among them is that they all are students that
read the newspaper each week. They are also all being measured based on how many
times they read the newspaper each week. When cases closely match, or the event is
measured twice, both parametric testing and non-parametric testing are used. When data
is derived from the ratio and interval measurements, parametric tests are generally used.
Conversely, non-parametric tests are typically utilized to test a hypothesis with ordinal or
nominal data sets. In this scenario, both tests could be applied. The t-test (non-
parametric) or z-test (parametric) can be used to show the lack of significant difference
between the 2 samples given.
I would use the z-test to make this determination and test this hypothesis. One
would use the z-test when the sample size is greater than 30 (Schindler, 2019, p. 376).
When performing this test, the p-value is shown to be less than .05; therefore, a
significant statistical data set does not exist and the hypothesis is preserved. For example,
“A P value of 0.05 carries a 5% risk of a false positive result (i.e. there is no true
difference between treatments). If a trial is meant to provide proof of a genuine treatment
difference beyond reasonable doubt, a much smaller P vale – say p< 0.001 – is required”
(O’Donnell, 2018, para. 4). The p-value results in the conclusion that there is no
significant difference between liberal arts and marketing students. Similarly, and
biblically, there is no difference between those who choose to give their lives to Christ.
Romans 10:12 says, “For there is no difference between the Jew and the Greek: for the
same Lord over all is rich unto all that call upon him” (KJV). Christ died for each of us,
regardless of our background, race, or preferences in life.
References
Khalilzadeh, J. & Tasci, A. D.A. (2017). Large sample size, significance level, and the
effect size: Solutions to perils of using big data for academic research. Tourism
Management, Elsevier, Vol. 62(C), pages 89-96.
O’Donnell, J. L. (2018, March 6). P-value. What value? Retrieved from https://doi-
org.ezproxy.liberty.edu/10.1111/imj.13723
Schindler, P. S. (2019). Business research methods (13th ed.). New York, NY: McGraw-
Hill.
Describe the relationship between the two variables in the four plots.
An important, effective, and impactful way to interpret data is the use of
scatterplots. In short, scatterplots allow researchers, and those for which the research is
intended, to visualize the relationships between the information and data that is studied
throughout the research process. Put another way, “Scatterplots are essential for
understanding the relationships between variables. They provide a means for visual
inspection of data that a list of values for two variables cannot” (Schindler, 2019, p. 398).
Furthermore, in order for scatterplots to be effective, they must be accurately
interpreted by managers and researchers alike. In order to reach this goal, typically three
patterns are analyzed to determine relationship, “The overall pattern of a scatterplot can
be described by the direction, form, and strength of the relationship” (Mindrila and
Balentyne, 2013, p. 5). For example, the information in the images shown in this question
can be broken down into direction, form, and strength of relationship below:
The first image, scatterplot a, would most accurately be described as not having a
relationship, or r=0. Conversely, there is a possibility that a non-linear relationship may
exist to explain the data presented in the scatterplot.
1. Direction: None.
2. Form: None.
3. Strength: 0.
The second image, scatterplot (b), would best be described as having a positive
relationship. A simpler way to make this point is to notice that when X increases, so does
Y. Additionally, a straight line can be drawn through the data to show relationship.
1. Direction: Positive.
2. Form: Linear.
3. Strength: An estimation can be given between 0.3 and 0.4 (no true scale
given).
4. Analysis Technique Used: Pearson, or product moment, correlation
coefficient.
In this case, “The Pearson (product moment) correlation coefficient varies over a range of
+1 through 0 to -1. The designation r symbolizes the coefficient’s estimate of linear
association based on sampling data” (Schindler, 2019, p. 396).
The third image, scatterplot (c), shows a curvilinear relationship to the line. This
means r is unsuitable to measure the relationship between the rest of the data.
1. Direction: positive at first, then negative shift.
2. Form: Curvilinear.
3. Strength: Unable to determine scale.
4. Analysis Technique Used: Correlation ratio.
In the case of a curvilinear scatterplot, “A relationship that has the form of a
curve, rather than a straight line, is due to the fact that one variable does not increase at a
constant rate and may even start decreasing after a certain point” (Mindrila and
Balentyne, 2013, p. 7). In short, as X and Y begin on a positive slope, at some point the
variables begin to decline in the same way.
The fourth image, scatterplot (d), would best be described as having a negative
relationship and following a straight line throughout the data set.
1. Direction: Negative.
2. Form: Linear.
3. Strength: An estimation can be given between -0.8 and -0.9 (no true scale
given).
4. Analysis Technique Used: Pearson, or product moment, correlation
coefficient.
References
Mindrila, D. & Balentyne, P. (2013). Scatterplots and correlations. Retrieved from
https://www.westga.edu/academics/research/vrc/assets/docs/scatterplots_and_corr
elation_notes.pdfNassaji, H. (2019).
Schindler, P. (2019). Business research methods (13th ed.). New York, NY: McGraw-Hill.
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