Answer

1. • Quantitative Methods and Analysis-Discussions

     QUESTION ONE

     Discuss how statistics, as a way of organizing and summarizing data, helped you make good decisions when shopping, selecting a place to live, or planning your budget for the next month.

     ANSWER

     Statistics is critical for organization and summary of data as well as decision making in various settings. In particular, nonparametric data by Weihs and Ickstadt (2018) idealize statistical analysis an effective tool for interpretation of data and forecasting of future scenarios, in both academic and industrial settings. Three statistical methods for good decision making are delimited from extant literature:

     Hypothesis testing

     Hypothesis testing is typically applicable to the transformation of “data driven problems” into hypotheses to facilitate understanding of logical connections between concept and statistics. For instance, when shopping, selecting a place to live, or planning your budget for the next month, statistics is essential for understanding connections between mean household income and tenancy in specific locations. These connections make use of “statistical hypotheses” and analysis which facilitate “statistical testing” of questions and theory to derive meaningful information (Weihs & Ickstadt 2018). To apply hypothesis testing to decision making, it is necessary to adjust significance levels of repeatedly used data to forestall the possibility of errors.

     Regression Analysis

     Regression analysis is a statistical tool for approximation of connections between dependent variable and independent variables, generally defined as the input data that is intended to impact the dependent variable. The analysis could potentially be Available data has shown positive correlation between standards of education attainment and living standards (Weihs & Ickstadt, 2018).

     Time series analysis

     Time series is another statistical tool for modeling and forecasting sequential phenomena. For instance, time series are useful for predictions involving “observational data” (Weihs & Ickstadt, 2018). While these tools are typically useful for statistical modeling of social science variables, the tool is mostly important for forecasting of relationships of “the time series itself or of its properties” (Weihs & Ickstadt, 2018). For instance, time series may be applied to delineate the impact of lease duration on rental costs. Specifically, time series data may disclose a pattern in which predictions of lower rent costs may apply for longer lease periods.

      

     QUESTION TWO

     Discuss how likely it is that 70% of students will pass this course with a B or an A. Then, consider the following questions:
     1. Would you look at data showing the success rate of previous courses?
     2. Would you check whether the current GPA of students in your class is high or low?
     3. What other data would you like to have before you determine the probability of 70% of students passing this course with a B or an A?

     ANSWER

     Many subjective tests are mediated by improbability. As a result, tests in which the probability of students passing a course with a B or an A is 70% should be subjected to statistical treatment to derive meaning from them. Essentially, probability determination will begin by apportioning a probability space of 0 and 1. 0 suggests that the intended outcome will not occur while 1 confirms the certainty of the outcome (Srinivasan, Alu-Srinivasan & Schiller, 2016; Spiegel, 2016). In the scenario under consideration, a probability of 70% is inferred, meaning the outcome has a 3 to 10 probability of not occurring. While pertinent data on the success rate of previous courses may be important, there is evidence that the current GPA of students in the class may prove far more useful for determination of probability. To achieve this, two popular methods are applicable:

     The classical approach:

     This structures the likelihood of occurrence to a number of ways, say, 7 different ways out of 10. If this is the case, then the probability is equated to 70%. This approach also suggests 3 out of 10 chance of the outcome not being realized.

     The frequency approach:

     This is anchored on outcomes of repetitive tests to sustain a clear pattern of scores. Assuming that a large number of tests are conducted, then the desired outcome may be assigned to occur h times out of a probability space of n. this method of calculation of probability is called empirical probability of the event. Applying the preceding scenario to our desired outcome of 70%, it may be inferred that if 10 tests should consistently yield a score of 70% and above.

     While both methods have grave drawbacks, evident from the use of words “equally likely” and a “large number” in classical and frequency approaches respectively, most statisticians have shown preference for “axiomatic methodology to probability” (Srinivasan, Alu-Srinivasan & Schiller, 2016).

     QUESTION THREE

     Is average income the same as median income?

     ANSWER

     The “mean and median” are two of the most popular measures deployed in the demarcation of “the center” of frequency distributions as well as in the representation of household incomes (Donovan, 2020). The studies further define mean as the average income or “total aggregate household income by the total number of households, that is, the simple average or the level of income that each household would have in hand if total income were distributed equally”.  The mean is most significant for evenly distributed data (as observed in regular distributions) but remains ineffective for interpretation of distributions with several outliers (Donovan, 2020).

     While the mean is a popular metric in the determination of central tendency, the median is widely regarded as the most accurate determinant of archetypal household data. Essentially, it is calculated by dividing the distribution into two equal data sets: one with the lowest 50% of households with less than the median income, and the top 50% of household’s incomes in the upper half of the distribution. 

     In most calculations, values of mean and median are often different. For instance in mean and median household income data for the State of Florida are US$85,581.31 and US$58,150.00 respectively (PK, 2020). However, Florida is not the only case with such variance. In fact, these trends are evident from the United States Census Bureau data which puts the US median household income at $51,939 in 2013 while the mean household income was $72,641 during the period under review (Donovan, 2020).

                 To explain this anomaly, we take a hypothetical situation in which eight families each with “annual income of $52,000”, effectively rendering “median and mean annual income” to be $52,000.  Consider a situation in which one of the families win a lottery, pushing its income to $200,000 for the year, then the median value will remain unchanged while the mean income will balloon to US$66,800.00 (Donovan, 2020). These findings are consistent with average and median household income in Maryland which stands at US$125,053.40 and US$95,310.00 respectively (PK, 2020).

     QUESTION FOUR

     Provide an example of the null hypothesis and a corresponding example of the alternative hypothesis. Please use examples related to business or school activities.

     ANSWER

     Travers, Cook and Cook (2017) define hypotheses as “propositions or conjectures” that are advanced using partial data or educated guesses. In many studies, the postulations are made prior to a study, and generally provide “testable predictions” as a crucial part of scientific inquiry. In advanced research, it is customary to have several hypotheses during the introductory parts of research papers or dissertations (Travers, Cook & Cook, 2017). For instance, a researcher may propose that literacy intervention improves eloquence among learners with autism. Consequently, prior to the administration of the proposed remedy, it may be prudent to make an educated guess.

     Two main types of hypothesis can be delineated from extant literature, namely, null hypothesis and alternative hypothesis.

     A null hypothesis essentially states that research outcomes will not be impacted by the dependent variables. In other words, “there will be no differences between intervention and control groups in oral reading fluency at the end of the study” (Travers, Cook & Cook, 2017). This hypothesis is testable and could be approved or disapproved.

     On the other hand, alternative hypothesis proposes that research outcomes will have an impact on dependent variables. For instance, a proposition those learners with autism “receiving the oral reading fluency intervention” will demonstrate superior literacy capability than their colleagues who did not.

     The alternative hypothesis could present a feasible justification for study findings in researches in which the null hypothesis is overruled, yet lacking empirical basis. The outcomes could also be statistically important as it shows that the outcome is mathematically improbable should the null hypothesis be validated. To put it differently, if the variations in “oral reading fluency between control and intervention group are statistically important, there would be a noteworthy variance between groups could provide a basis for rejection of the null hypothesis” (Travers, Cook & Cook, 2017).

     QUESTION FIVE

     Describe the purpose of scatter diagrams, and discuss how you would determine whether positive, negative, or no correlation exists between two variables by looking at the scatter diagram.

     ANSWER

     The scatter diagram is a statistical tool is essential for investigating connections between variables. They are generally important for representation of data using 2 dimensional graphs in which dependent variables are plotted on one of the axes while the independent variable is presented on the other. Data from both axes typically intersect within the graphs to reveal visual trends and relationships. Thus, they provide visual evidence of “cause-and-effect relationships” which they can be used to approve or disapprove. Though scatter diagrams provide evidence of trends and patterns, they do not prove causation (Travers, Cook & Cook, 2017). Apart from establishing probable cause and-effect connections, these diagrams could prove commonality in the origin of two variables particularly if both causes at least one of the causes is unknown.

     To construct a simple scatter diagram, accumulate “paired data” from several samples, numbering about 50. Assign two dimensions for every “observation point”. For example, if your research is anchored on the proposition that there is a connection between “the age of patients and the length of their recovery time”, an representative data of 50 patients could include personal details such as age and durations of their recovery (Travers, Cook & Cook, 2017). Next, sketch the diagram showing “causes on the horizontal axis and probable impacts on the vertical axis. Delineate the “measures and changes” and label each line. Observe and record observations to identify important relationships. in this case, a probable relationships could  be that “patient age has an impact on recovery time”, with patient age on the horizontal axis. Subsequently, present your findings on the scatter diagram. Finally, deduce important patterns and meaning from the results paying special attention to the “width and tightness of the scatter” (Travers, Cook & Cook, 2017)

     These diagrams do not prove a “cause and effect relationship” but are essential for showing the robustness of the two variables. The stronger the relationship suggested, the greater the likelihood that a change in one of the variables will affect a change in the other. the main types of scatter diagrams are presented below:

     Figure 1: A positive correlation

     Source: National (2018)

     Recovery times are likely to increase as patient age increases.

     Figure 2: A possible positive correlation

     Other variables in addition to patient age may affect recovery time.

     Source: National (2018)

      

      

     Figure 3: No correlation

     There is no demonstrated connection between patient age and recovery time

     Source: National (2018)

     Figure 4: A possible negative correlation Other variables in addition to patient age may affect recovery time.

     Source: National (2018)

     Figure 5: A negative correlation

     This diagram suggests that recovery time is likely to decrease as patient age increases.

     Source: National (2018)

Answer

Al Gore’s “An Inconvenient Truth” Movie Analysis

            While delivering a speech, persuasion is essential in convincing the audience to listen to their ideas in their address. In An Inconvenient Truth, former US Vice President Al – Gore speaks on global warming as an encroaching crisis affecting its atmosphere and the environment as his central message. Al- Gore effectively persuades the audience into joining his cause against global warming by using persuasive communication strategies, a solid introduction, rhetoric strategies, oral citations, proper speech delivery, and presentation aids to evoke the audience in supporting his cause.

            Al- Gore’s successfully incorporates a solid speech introduction to attract the audience’s attention. He begins the introduction with a joke alluding to him being the “former future president of the United States.” The use of such a satirical comment evokes the audience wondering who would be bold enough to stand on stage after losing a race, such as the presidential election. This captures the audience to be more involving in his speech and sit for a better listening into the matters at hand. Later on, he introduces his speech topic by focusing on his central message, outlining his whole address’s main points. Finally, it eases the audience by showing a mangrove parchment indicated to involve the audience in relating to a preserved environment before expounding on his speech. The audience is engaged after this as he gets into his central message and further engaging in his speech.

Al-Gore’s excellently persuades the audience by using ethos as a rhetorical strategy throughout the speech.  Ethos employs a sense of trustworthiness and competence that enables the audience to believe in the speaker’s credibility. He shows ethos by acknowledging his commitment to the earth as an environmental activist. Al- Gore’s speech is based on expansive research that helps the audience trust his competence in speaking on the issue. Al- Gore’s possesses charisma and positive energy that attracts the audience to remain rooted in listening to his appeal towards addressing global warming. As characteristics of applying ethos in a speech, the combination of dynamism and competence draws the crowd to become trustworthy with his presentation and remains attentive throughout the address.

Al- Gore’s effectively employs persuasive communication strategies that include positive motivation, negative motivation, cognitive dissonance, non-verbal communication, and appeals to self-esteem in his speech. Positive and negative motivations are essential in persuading the audience to venture into addressing global warming to achieve positive outcomes in the environment. Consequently, Al-Gore uses negative motivation to convince the audience that failure to look into measures of curbing global warming and climate change, the earth might end up like the few places he depicts in his comparison photographs and videos. Cognitive dissonance helps change one’s perspective to something by discomforting norms and beliefs to persuade an audience towards change. At the start of the documentary, Al-Gore introduces a short video of a beautiful mangrove parchment that would stay in the back of the audience’s mind on what should be safeguarded.  To destabilize the audience, he shows pictorials of areas devastated by global warming, evoking fear and panic for the world that has become dormant in addressing this issue. Intertwined, with his central idea, Al- Gore persuades the audience in a bleak and disheartened tone to fight for preserving the environment.

            In addition, Al-Gore’s effectually uses non-verbal communication in his body language is established through a dejected worrying tone for identifying with the audience on the prevailing situation. Al- Gore’s body movement showed confidence in his walk and constant interactiveness with the audience. Al – Gore also has a confiden, genuine smile appearing as a well- groomed and dressed man in delivering his speech. In the documentary, Al-Gore’s clear expression of displeasure with people who negated around global warming instead of addressing is clear.  Al-Gore aimed to show concern for the issue. Al –Gore’s self-esteem pushes his central message across the audience by focusing on positivity and the audience’s contributions to curb global warming. His articulation of each point across helps in building confidence with the audience. His confidence in his speech persuades the audience to be on board the matter.

            Oral citations are well used in An Inconvenient Truth to capture the audience’s attention. Al- Gore uses oral citations effectively to show reliability, credibility, and validity of information conveyed in his speech address. Denoting empirical evidence from videos, charts, and maps allude the audience into believing that Al- Gore critically researched the issue and came up with a profound speech to convince the audience to join his cause to remove fallacies on wrong information presented in his speech. Virtually, his research pays off as he captures the audience in his factual interactions on the matter.

Al – Gore excellently uses presentation aids like projected images, comparison photographs, short videos, satirical cartoons, and info graphs like maps and charts to help persuade his audience to come to his plea in preserving the environment by combating global warming. Projected images show areas adversely affected by global warming, including flooded areas. The short videos as well show people injured due to flooding. The graphs and maps show empirical evidence of the effects of global warming in areas. A comparison of videos and pictures shows how some places were before global warming and its impact after years. All these visual aids serve as areas involving the audience’s concern and worry over the deteriorating ecosystem around us. Al-Gore was not shy off, including videos of politicians passing over the global warming issue through satirical cartoons while also poking at renowned scientists worldwide who showed the existence of climate change. As much as Al-Gore is a politician, he intended for the audience to understand that his concern was for the environment and endeavors towards combating global warming rather than politically-driven shows with aspirations of a political seat.

Lastly, Al- Gore successfully uses ethos, pathos, and logos strategies to capture the audience’s attention in his speech. Ethos employs a sense of trustworthiness and competence that enables the audience to believe in the speaker’s credibility. He shows ethos by acknowledging his commitment to the earth as an environmental activist. The documentary shows the incorporation of logos through his presentation of scientific facts that support his claims to global warming as an issue of concern. Lastly, his attributes to incorporate his son’s demise into comparing it to his commitment to the environment show pathos as a rhetoric strategy.  Successful integration of photographs and videos of areas affected by global warming helped provoke the audience to support his cause towards alleviating global warming.

In conclusion, Al – Gore effectively incorporates persuasive communication strategies, a solid introduction, rhetoric strategies, oral citations, proper speech delivery, and presentation aids to evoke the audience in supporting his fight against global warming.  Using all these techniques successfully convinces the audience to have a concern about the deteriorating ecosystem. Having watched the documentary, I am persuaded to carry on the legacy of conserving our environment as an environmental ambassador.         

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