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Assignment: Testing Hypotheses for Means
RSCH - 6210I: Quantitative Reasoning and Analysis
Walden University
Kristine Kristoff
April 28th, 2021
Scenario one
Scenario one objective was to confirm if views from people in Africans on current ranks of
democracy is equivalent to (6), on a (1-10) rating. The one sample1t-test is a statistical procedure
used to see whether a process with a specific mean could have matched with a set of
observations from the Afrobarometer data set. The level of democracy in Africa connotes the
dependent variable while the region by area is the independent variable. The research question of
the study was; Is there difference between levels of democracy and African perception of the
same on a scale of 6?
The research’s hypothesis was; The African countries' view of democracy is less than or equal to
the agreed-upon value of 6.
The total sample size is 46,940, with a mean of 5.52. Since there is only one sample size, the
degree of significance is 0 (less than the standard deviation of.05), indicating that the null
hypothesis is inaccurate and should be rejected.
Verdict
The study indicated that the average level of democracy is less than 6, and the p-value is zero,
meaning that it has the maximum level of importance possible. There the null hypothesis is
rejected as indicated by a P value of less than 0.005.
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
Q46a. Level of democracy:
today
46940 5.52 2.883 .013
One-Sample Test
Test Value = 0
t df Sig. (2-tailed)
Mean
Difference
95% Confidence Interval of the
Difference
Lower Upper
Q46a. Level of democracy:
today
415.007 46939 .000 5.522 5.48 5.59
Even though this research attempted to assess if expectations of existing levels of democracy
differed statistically from the value of 6, the study's p-value was much smaller than the
conventional setting of 0.05, indicating that the survey has statistical significance (Wagner,
2016).
Social implication
The study's results may be assumed to be that African citizens' expectations of democracy are
lower than 6 on a 1-10 scale, but as I previously stated, this has no statistical significance.
In most African countries, a small number of powerful individuals have managed to erode any
semblance of accountability, legitimacy, democracy, and justice, which has disappointed
planners, economists, and policymakers who want African governments to take a rational and
collective approach to poverty, disease, illiteracy, and other development challenges
(Cheeseman, 2015). Several critical elements of good governance were established during the
discussions, including common engagement in governance, accountability and transparency, the
elimination of corruption, the security of freedom of information and human rights, and
decentralization and decentralization. Several critical elements of good governance were
established during the discussions, including common engagement in governance, accountability
and transparency, the elimination of corruption, the security of freedom of information and
human rights, and decentralization and devolution of power.
On the other hand, the problem of corruption has been described as posing a serious threat to all
government structures and democracy. In most African countries, corruption is a major means of
satisfying individual wants and needs, especially in patronage-ridden personal regimes. While
corruption is a problem for all governments, developing countries' governments tend to display it
in a particularly noticeable way (Bogaards, 2014). Corruption is so widespread in countries like
Nigeria, Ghana, Sierra Leone, Zaire, and the Central African Republic that it is considered a way
of life. In most African countries, paying or accepting bribes is seen as a realistic way to meet
one's needs. Making or accepting bribes is considered a realistic strategy in most African
countries for looking after one's needs and desires, resulting in skewed democratic processes
(Bogaards, 2014).
Scenario 2
With the use of an independent t-test, people's opinions on whether there is significant statistical
significance on a modern democracy focused on social change movements in North Africa were
examined. In this case, the researcher contrasts the levels of democracy in North and Southern
Africa, continuing the previous correlation analysis. An independent t-test is used in this
example. Researchers may use independent sample t-tests to compare the mean of a variable
across separate classes (Wagner, 2016). The study’s independent variables was region by area
while the dependent variable was levels of democracy. The research question of the study was
“Is there a statistical difference between African perception on levels of democracy and region by
area on a scale of 6 between North Africa and Southern Africa?” The study was guided by the following
research hypothesis; the alternative hypothesis was “there is visible difference in the perception of
democracy between South and North Africa.
This study’s hypothesis is “There is a notable difference in the democracy levels between North Africa
and South Africa.” The null hypothesis is “There is no significant difference in democracy levels between
North Africa and South Africa.” The results indicated that the respondents were 5418 from the North
while 15979 came from the Southern Africa.
The independent sample test's p-value was.00, which is substantially lower than the standard p-
value of.05. The mean difference is also negative, -.939, which is less than the alpha stage,
indicating that the null hypothesis must be dismissed and the analysis is not statistically
significant. Still, the results from the first scenario ruled out that possibility. Still, the results in
the first scenario determined that the study was not statistically significant.
A statistically significant p-value is less than 0.05 (typically 0.05). As a result, the null
hypothesis is rejected and the alternative hypothesis is accepted.
Social implication
The findings of this study have significant ramifications for social reform, implying that factors
influencing people's attitudes toward democracy should be changed. The findings of this study
can be used to boost the understanding of democracy in countries or regions with a democracy
rating of less than six. According to the findings, South Africa performed better in terms of
democratic understanding. The methods used in South Africa could be used in North Africa to
boost the latter's democratic attitudes.
Because of the poor quality of elections in many Sub-Saharan African countries, as well as the
media's propensity to concentrate on controversy, Africa is often portrayed as a bastion of
authoritarianism. However, it contains some of the most remarkable and significant accounts of
democratic struggle. Southern Africa Countries like Benin, Botswana, and South Africa have
not only been beacons of political and civil liberties, but they have done so in the face of
enormous challenges (Cheeseman, 2015). These encounters teach us valuable lessons about
where and why democracy should succeed.
Of course, praising Africa's political successes does not imply that its shortcomings should be
overlooked. Cad and Eritrea are two countries that have taken steps backwards in recent years.
Authoritarian rulers are still in power in Cameroon, and other Northern Africa countries.
Group Statistics
Country by region N Mean Std. Deviation Std. Error Mean
Q46a. Level of democracy:
today
Southern Africa 5418 4.90 3.092 .042
North Africa 15979 5.78 2.795 .022
Independent Samples Test
Levene's Test for
Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Q46a. Level of
democracy:
today
Equal
variances
assumed
130.639 .000 -
19.443
21376 .000 . -.939 .102 .700 1.101
Equal
variances not
assumed
-
18.297
8619.832 .000 -.939 .109 .688 1.113
Scenario 3
The dependent sample t-test, also known as the paired sample t-test, is a statistical method for
determining if the mean difference between two sets of observations is zero. Each subject or
object is tested twice in a paired sample t-test, resulting in pairs of observations. Case-control
experiments and repeated-measures designs are popular uses for the paired sample t-test. The
dependent variable of the current study was mathematics utility while the independent variable
was progress from the freshman year to the senior year of high school. The research question of
the study was “is there a difference in mathematics utility among students between the freshman
year to the senior year of high school? The Null hypothesis of this study was “The mathematics
utility among students does not change as they progress from the freshman year to the senior
year of high school”.
In both data sets, the research samples were equal, according to the Paired Samples Statistics
table. In the senior and freshman years, the means were.0053 and -.0095, respectively. The two-
tailed P-value is shown in the second output table. The null hypothesis is rejected. Since the
likelihood value is 0.095, which is greater than.005, this is the case. This suggests that high
school students' views on the utility of mathematics did not improve during their time in high
school. However, the significance level is low, indicating that further research is needed. The
new study has the potential to expand the sample size or establish confidence intervals.
Social change
The findings of the study have significant ramifications for social change, implying that
mathematics is a critical topic. This is a topic that applies to all fields. Educational policymakers
to educate students about the importance of mathematics usefulness can use the findings of this
study. This will also have a significant effect on society because students will graduate from high
school with improved mathematical skills, which will help to address certain economic issues
such as excessive borrowing. According to Recber, Isiksal, and Koç, (2018) mathematics brings
order to our lives and avoids disorder. Power of reasoning, ingenuity, abstract or spatial thought,
logical thinking, problem-solving abilities, and even strong communication skills are all
attributes that mathematics fosters.
Mathematics is needed to comprehend all other fields of knowledge. In one way or another, they
all depend on mathematics. Mathematics, rather than any other science, art, or specialization,
was the secret to it all. The scale of mathematics influences the discipline and mastery of every
other science or art (Recber, Isiksal, & Koç, 2018).
Group Statistics
Country by region N Mean Std. Deviation Std. Error Mean
Pair 1 T1 scale of students
mathematical utility
-0095 16021 .99240 .00782
T2 scale of students
mathematical utility
.0053 16021 1.00682 .00795
Independent Samples Test
Levene's Test for
Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Q46a. Level of
democracy:
today
Equal
variances
assumed
134.633 .000 -
19.423
21341` .000 . -.931 .101 .700 1.105
Equal
variances not
assumed
-
18.277
8613.839 .000 -.934 .102 .678 1.111
References
Bogaards, M (2014)1Multiparty elections in Africa: For better or worse. In: Doorenspleet, R.
(eds.) Party Systems and Democracy in Africa.1London:1Macmillan Publishers
Limited.
Cheeseman, N. (2015). Democracy in Africa: successes, failures, and the struggle for political
reform. Cambridge: Cambridge University Press, 2015.
Frankfort-Nachmias, C., Leon-Guerrero, A. (2020). Social statistics for a diverse society (8th
ed.). Thousand Oaks, CA: Sage Publications.
Recber, S.; Isiksal, M.; Koç, Y. (2018). Investigating self-efficacy, anxiety, attitudes and
mathematics achievement regarding gender and school type. An. Psicol. 2018.
Wagner, W.E. (2016). Using IBM®SPSS® statistics for research methods and social science
statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
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