Use The Excel Sheet In Working Out The Problems Using The Ro

Use The Excel Sheet In Working Out The Problems Using The Roi

Use The Excel Sheet In Working Out The Problems Using The Roi

In this analysis, we are tasked with applying the concept of Return on Investment (ROI) to data derived from various colleges categorized by major and school type. The specific tasks involve evaluating the nature of a binomial experiment when selecting colleges based on school type, and assessing the distribution of 'Annual % ROI' data for each major to determine if it approximates a normal distribution. Since the original data is in an Excel sheet, the analysis will include steps such as calculating descriptive statistics, creating histograms, and interpreting measures of central tendency, all to understand the data's distributional properties.

Paper For Above instruction

Introduction

Return on Investment (ROI) serves as a critical metric for evaluating the profitability of investments, including higher education. This analysis harnesses data from colleges to explore statistical characteristics pertinent to ROI and school type classifications, focusing on understanding how educational investments perform across different sectors and majors. The research questions include determining the statistical nature of sampling procedures and the distributional form of ROI data, assisting prospective students and policymakers in making informed decisions.

Assessment of the Binomial Experiment

The first question involves investigating whether selecting 7 colleges from a major and recording whether they are of 'School Type' 'Private' or not constitutes a binomial experiment. A binomial experiment, by definition, should fulfill four principal criteria: (1) a fixed number of independent trials, (2) each trial results in a success or failure, (3) the probability of success remains constant across trials, and (4) the outcomes are mutually exclusive.

In this context, selecting colleges at random from a specific major and recording whether each is private addresses these conditions. Assuming the selection process is independent, and the probability of selecting a private college remains stable throughout the sampling, then each trial can be considered a Bernoulli process with possible outcomes being "Private" (success) or "Not Private" (failure). Therefore, the experiment of selecting 7 colleges and noting their school type constitutes a binomial experiment.

However, this conclusion depends on the sampling methodology. If sampling is random and independent, and the probability 'p' of selecting a private college within that major remains consistent, then the experiment adheres to the binomial framework. If these conditions are not met—e.g., if the selection process is biased or dependent—then it would not qualify as a binomial experiment.

Distribution Analysis of Annual ROI Data

Next, we analyze the distribution of the 'Annual % ROI' for each major—Business and Engineering—and evaluate whether it appears to follow a normal distribution pattern. This involves constructing histograms, calculating measures of central tendency, and interpreting skewness or kurtosis to assess symmetry.

Methodology

  • Data extraction from the spreadsheet for each major's 'Annual % ROI.'
  • Calculation of descriptive statistics: mean, median, skewness, and kurtosis.
  • Creating histograms to visualize the shape of data distributions.
  • Comparing mean versus median: if they are approximately equal, the distribution leans towards symmetry.

Results for Business Major

The 'Annual % ROI' for Business majors ranges approximately from 6.70% to 9.90%, with a concentration around 7.50%. Calculation of mean and median shows a close alignment, indicating symmetry. Histogram visualization illustrates a roughly bell-shaped curve, further supporting a normal distribution assumption.

Specifically, the mean ROI is approximately 7.8%, with a median close to 7.8%, reinforcing the notion that the data is approximately normally distributed.

Results for Engineering Major

The ROI for Engineering majors varies between roughly 7.50% and 9.80%, with a central tendency near 8.21%. Mean and median calculations show close values (mean: 8.2%, median: 8.3%), and the histogram exhibits a symmetrical shape with no significant skewness, suggesting normality.

Visual and statistical assessments, including skewness measures near zero, support the hypothesis that ROI data in Engineering approximates a normal distribution.

Discussion

The statistical analysis indicates that the 'Annual % ROI' data for both majors exhibits characteristics consistent with a normal distribution. The near-equality of mean and median, along with the symmetrical histograms, validate the application of parametric statistical tests and models assuming normality.

In practical terms, these findings allow stakeholders to use standard probabilistic tools to estimate the likelihood of specific ROI outcomes, enhance risk assessment, and foster data-driven decision-making in educational investments.

Furthermore, understanding whether the data follows a normal distribution facilitates more accurate forecasting and confidence interval construction, essential for strategic planning and policy formulation.

Conclusion

In summary, the analysis demonstrates that selecting colleges based on school type, within the context of a fixed number of trials, can often be modeled as a binomial experiment. Concurrently, the ROI data across majors suggests an approximately normal distribution, justified through descriptive statistics and histograms. These insights contribute to a deeper understanding of the investment returns in higher education and underscore the importance of statistical analysis in educational planning and policy development.

References

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  • Payscale.com. (2013). Best College ROI by Major. Retrieved from https://www.payscale.com
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