Central limit theorem: Applications in business analysis
Order ID |
53563633773 |
Type |
Essay |
Writer Level |
Masters |
Style |
APA |
Sources/References |
4 |
Perfect Number of Pages to Order |
5-10 Pages |
Description/Paper Instructions
Central limit theorem: Applications in business analysis
The Central Limit Theorem (CLT) is a fundamental concept in statistics that plays an important role in business analysis. The theorem states that the sampling distribution of the means of a large number of independent and identically distributed random variables will be approximately normal, regardless of the underlying distribution. In this blog, we will discuss the applications of the Central Limit Theorem in business analysis.
Overview of the Central Limit Theorem
The Central Limit Theorem states that if you take a large sample from any population with a finite mean and variance, the distribution of the sample means will follow a normal distribution. This is true regardless of the shape of the population distribution.
The theorem is essential in statistics because it allows us to use a sample to make inferences about the population mean. In business analysis, this theorem is especially important because it allows us to draw conclusions about a population using a sample, which is often much more practical and less expensive.
Applications of the Central Limit Theorem in Business Analysis
Estimating Population Mean
The Central Limit Theorem plays a vital role in estimating the population mean in business analysis. For instance, a marketing researcher may use a survey to collect data on customer satisfaction levels. Instead of surveying every customer, which can be expensive and time-consuming, the researcher can use a sample of customers and apply the Central Limit Theorem to estimate the population mean of customer satisfaction.
Hypothesis Testing
The Central Limit Theorem is also used in hypothesis testing in business analysis. Hypothesis testing is the process of testing a claim or assumption about a population parameter. For instance, a business owner may want to know if the mean waiting time for customers at their store has decreased after introducing a new queuing system. To test this hypothesis, the business owner can collect a sample of waiting times, calculate the sample mean, and use the Central Limit Theorem to determine the likelihood of observing the sample mean if the waiting time has not changed.
Confidence Intervals
Confidence intervals are another important application of the Central Limit Theorem in business analysis. A confidence interval is a range of values that is likely to contain the true population parameter with a specified level of confidence. For instance, a market researcher may be interested in estimating the average income of a particular demographic. To create a 95% confidence interval, the researcher can collect a sample of incomes and use the Central Limit Theorem to construct a confidence interval for the population mean.
Quality Control
The Central Limit Theorem is also applied in quality control in business analysis. For instance, a manufacturing company may be interested in ensuring that the weights of their products are within a certain range. To ensure this, the company can use statistical process control (SPC) techniques to monitor the production process. SPC relies on the Central Limit Theorem to ensure that the distribution of the weights of the products is normal, which is essential for setting control limits.
Portfolio Analysis
The Central Limit Theorem is also applicable in portfolio analysis in finance. Portfolio analysis involves analyzing a collection of assets or securities to determine the expected return and risk of the portfolio. The Central Limit Theorem is used to calculate the expected return and risk of the portfolio. By applying the Central Limit Theorem, investors can estimate the probability of realizing certain returns from a portfolio and develop a suitable investment strategy.
Conclusion
In summary, the Central Limit Theorem is a fundamental concept in statistics that plays a vital role in business analysis. It enables researchers and analysts to use a sample to make inferences about the population mean and variance, perform hypothesis testing, construct confidence intervals, and control the quality of products. The Central Limit Theorem is also applicable in portfolio analysis in finance. By applying the Central Limit Theorem, businesses can make informed decisions that are based on
Central limit theorem: Applications in business analysis
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Content (worth a maximum of 50% of the total points) |
Zero points: Student failed to submit the final paper. |
20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. |
30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. |
40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. |
50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. |
Use of Sources (worth a maximum of 20% of the total points). |
Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. |
5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. |
10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. |
15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. |
20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. |
Grammar (worth maximum of 20% of total points) |
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5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors |
10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors |
15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. |
20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. |
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3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. |
5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper |
7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. |
10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. |
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