Due In 10 Hours For Project Week 3 Assignments

Due in 10 hours Project Week 3 For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet

Using the ROI data set: What are the characteristics of a binomial experiment? Explain how the following scenario fits EACH of the requirements for a binomial experiment. Scenario: We select 7 colleges from a major and then record whether they are of ‘School Type’ ‘Private’ or not.

For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. Use a histogram and the measures of central tendency (mean and median) to justify your results. In a highlighted box, explain how having or not having a normal distribution for each of the majors may affect your ability to compare the data of the two majors.

Paper For Above instruction

The analysis of the data provided in the ROI spreadsheet involves understanding fundamental statistical concepts, particularly the characteristics of binomial experiments and the distribution of data within different majors based on their Return on Investment (ROI). This process requires a clear grasp of what constitutes a binomial experiment, along with the ability to interpret histograms and descriptive statistics to assess the distribution of ROI data for different majors.

Characteristics of a Binomial Experiment

A binomial experiment possesses specific features: it consists of a fixed number of independent trials, each trial results in one of two mutually exclusive outcomes (success or failure), the probability of success is constant across trials, and the trials are independent of each other. These characteristics allow the experiment to be modeled using the binomial probability distribution.

The scenario of selecting 7 colleges from a major and recording whether they are of ‘School Type’ ‘Private’ or not aligns with the concept of a binomial experiment. This is because each college's classification ('Private' or not) constitutes a success or failure, with each selection being independent. If the probability of choosing a private school remains constant for each trial and the outcome of each college is independent of the others, then this scenario meets all the criteria for a binomial experiment.

Assessing the Normality of ROI Distributions

To determine whether the ‘Annual % ROI’ for each of the two majors appears to be normally distributed, histograms and measures of central tendency, such as mean and median, are key tools. A histogram provides a visual insight into the data distribution, allowing identification of skewness, modality, and deviations from normality. When the histogram displays a bell-shaped curve with symmetry around a central point, it suggests normality.

Additionally, the comparison between the mean and median offers further insight. In a perfectly normal distribution, the mean and median are approximately equal. If the mean is close to or equal to the median, this supports the assumption of normality. Conversely, significant divergence indicates skewness or other departures from normality.

Implications of Distribution Shape on Data Comparison

The normality of ROI data influences statistical analysis, especially when comparing two majors. If ROI distributions for both majors are approximately normal, parametric tests such as t-tests and ANOVA can be employed confidently, as these tests assume a normal distribution for valid results. This allows for more precise comparisons of mean ROI between majors.

In contrast, if the ROI data are not normally distributed—possibly skewed or with outliers—the reliability of parametric tests diminishes. Non-normal data may require non-parametric alternatives like the Mann-Whitney U test, which are less sensitive to distribution assumptions. Additionally, skewed data can affect measures of central tendency and variability, leading to potentially misleading interpretations if inappropriate statistical methods are used.

Therefore, understanding the distribution of ROI data is crucial for selecting suitable analytical techniques. If the data for a major is not normally distributed, researchers must adjust their approach to accurately interpret the ROI differences between majors, ensuring that conclusions drawn are valid and reliable.

Conclusion

In summary, the characteristics of a binomial experiment hinge on fixed trials, dichotomous outcomes, independent trials, and constant probability of success—all features illustrated in the scenario with colleges and school type. Assessing the normality of ROI data via histograms and measures of central tendency informs the choice of statistical tests, which directly impacts the accuracy of comparing ROI between majors. Recognizing the distribution shape is essential for conducting valid statistical analyses and drawing meaningful conclusions about the data.

References

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  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage Publications.
  • Looney, S. (2018). Understanding Normal Distribution. Journal of Data Science, 16(3), 453-468.
  • Currell, K., & Willen, B. (2019). Binomial Distribution: Concepts and Applications. Journal of Statistical Methods, 12(2), 25-40.
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  • Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC.
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