Increasing efficiency by decreasing processing time

Answer

1. • Hypothesis Testing

     Statistical Hypothesis Testing

     Hypothesis analysis can be used in the scenario provided to resolve the problem of reducing processing time per document. According to the case of the Foreclosure department, the average number of documents processed per hour is 15.11 with a standard deviation of 2.666. On average, it takes 238.25 seconds to review one document. The experiment was conducted and shown that processing time reduced per document to 190.58 for a large monitor. Therefore, the mean processing time for the sample is less than population processing time. However, what is not known is known is whether these differences in average processing time for sample and population is statistically significant. It is believed that a large monitor would reduce average processing. It is important to assess whether this reduction was chance by chance or not through hypothesis testing. This paper seeks to determine whether this reduction in processing time is statistically significant at 5 percent.

     Step 1: Stating Hypothesis

     The five steps of hypothesis testing begin by stating null and alternative hypotheses: Null hypothesis represents no relationship or no effect whereas alternative hypothesis represents an observed relationship of effect (Selvamuthu, & Das, 2018). In the given scenario, we want to test that reduction in document processing time is not statistically significant.

     Null hypothesis: The accepted fact is that the population average processing time is 238.25 hence

     H₀: μ=238.25

     This indicates that average processing time would remain the same even using a large monitor to review documents.  In other words, a reduction in average processing time was due to a chance rather than the intervention. Therefore, changing to using a large monitor would not reduce the average processing time for documents.

     Alternative hypothesis: It is claimed that using a larger monitor has a less average processing time per document, so

     H₁: μ<238.25:

     We are testing the hypothesis that mean of the sample is significantly less than the mean of the population hence the average processing time of 190.58 seconds(sample mean) is significantly lower than the population average of 238.25 seconds. This means that intervention (large monitor) reduces waiting time.

     The fact that we are assessing whether the scores are “less than” a given point (238.25 seconds) implies that this is a one-tailed test. Besides, since we are determining whether the average processing time ‘less than’ 238.25 seconds, the tail is on the left side of the pick (Selvamuthu, & Das, 2018). The following picture visualizes the problem under investigation.

     Step 2: Determining the Significance level

                 In statistics, a standard deviation is a measure of spread, used to measure how a given number spreads out the mean or median value. It is used to measure the dispersion or variation of values. Typically, a higher SD means that values are extensively spread from the expected value (mean), while a lower value of SD reveal that values are close to the expected value in a given set (Selvamuthu, & Das, 2018). Normally, the SD of the population is denoted as while S denotes the sample SD. In the given case, the DS for the population: σ = 2.666 for meaning that means average document processed per hour range between 15.11±2.666. This means that the average number of documents processed per hour range 12.444 and 17.776 documents.

                 A random variable is the expected value, and often refers to the mean or median value from a set of values. It is a variable whose value is unknown and can be a continuous or a discrete value. They are used in statistics to outcomes of random occurrences. The random variable in the scenario is 238.25 seconds as the expected value.

                 There are two types of statistical tests commonly used to test the research hypothesis; these are z-test and t-test (Tacoma et al, 2020). Normally, the z test is applied in comparing the mean of the population to the with sample mean. However, the t-test is for comparing two or more sample means. The Z tests are used when the population mean is known is or when the sample exceeds 30 even when population mean is not known. However, for a sample size less than 30, we use t tests even when the population SD is not known. The difference from Z test, student t test is only used when the SD for the population is not known but rather the sample SD is known. The formulae for z and t scores are given as follows:

     Z score = x̄ - μ/σ√n

     t -score = Z score = x̄ - μ/s√n

     The following information is available from the scenario.

     Population mean: μ = 238.25 seconds

     Sample mean:      x̄ = 190.58 seconds

     Population standard deviation: σ = 2.666

     Sample size:      n = 20

     The T-test is the relevant testing formulated hypothesis from the scenario because the sample size is less than 30 (Selvamuthu, & Das, 2018). In hypothesis testing, significance level is described as the probability to make a wrong decision when null hypothesis is true. As noted by Andrade (2019), there are three levels of significance commonly used in statistics, these levels include 1%, 5% and 10%.

     Significance level = 0.05

     This level of significance is medium and the most used in statistical analysis. A significance level tells whether the difference in sample and population mean is due to intervention or by chance. The formula for degrees of freedom for a number of reviewed files in the given as n-1, and given the sample size of 20 in the given scenario,

     Degree of freedom =20-1 =19.

     The critical value is helpful determining whether the difference is statistically significant by comparing critical value with test statistic. If the calculated statistic is greater than the critical value from the t-table or z-table, then the difference in the mean is statistically significant and we reject the null hypothesis. However, if the calculated statistic is less than the critical value, the null hypothesis is not rejected. Note that critical value is derived from t-table and shown by the intersection of 0.05 significance levels and d. f of 19 (n-1). In this case, one-tailed is used to get the intersection point.

     Step 3: Calculate the Test Statistics

                 t -score = Z score = x̄ - μ/s√n

                                         = 190.58 – 238.25/2.666√20

                                         = -45.67/2.666x4.472

                 Test Statistics = -3.831.

     Note that the negative values representing the left tailed directional hypothesis.

     Step 4: Comparing Calculated Test Statistics and the Critical Value

     Test statistics is greater than critical value from t- table (Tcal = -3.831 > Tα, -1.729). Note that an area 0.05 is equal to 1.729 for t scores. The critical value is the intersection of significance level and degrees of freedom on t-table. As shown in the figure above, shaded is the rejection area representing 5% of the total area of the curve (Selvamuthu, & Das, 2018). The un-shaded is acceptance area hence critical values within this region imply accepting the null hypothesis.

     Step 5: Reach a Conclusion

     Since test statistics is greater than the critical value, we reject the null hypothesis that difference that population means is equal to 238.25. Difference in the mean of the sample and population is statistically significant. In other words, the test indicates that a reduction in processing time or documents from 238.25 to 190.58 significant. In light with these results, we are 95% confident that changing to large monitor increases processing efficiency leading to the reduced processing time for documents (Tacoma et al, 2020). Therefore, the manager was correct to conclude that using large-sized monitors will reduce the time taken to process one document.

     Conclusion

     Hypothesis testing was applied in the scenario to resolve the problem of whether changing to a large monitor increases operational efficiency and reduce the time taken to process documents in the Foreclosure Department. On average, it takes 238.25 seconds to review one document. The sample mean processing time was less than population processing time and this was found to be statistically significant. The significance level was set at 5% or 95%confidence level implying a 5% chance of error for the results. The null hypotheses stated that average processing time would remain the same even when using a large monitor to review documents. The results found a higher test statistics than critical value hence the null hypothesis was rejected. In conclusion, change to using large-sized monitors will reduce the time taken to process one document.

      

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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