Application Of Quantitative Methods In Business

Application Of Quantitative Methods In Business

Instructions QMB3200 Application of Quantitative Methods in Business Name of Student Completing This Assignment Interim Assignment Oriana Nunes Prof. Gladys E. Simpson Version: Fall 2017 This is an individual assignment data Student# # Definitions Gender female ClassLevel sophomore Age 20 GPA 3.5 HasStudentLoan no LoanBalance NA This Excel file contains several worksheets that have specific questions (10 total). You can add additional worksheets if needed to include supplemental material. View Instructions / video demo The video features a similar exercise completed in prior semesters Spring 2016 Q&A Session - Loan Questions mailto: [email protected]

The data below is fictitious and has been created using formulas to generate different Class Levels Gender values for each column of data for each file.

Data:

  • 1 Freshman 1 Female
  • 2 Sophomore 2 Male
  • 3 Junior 2 Female
  • 4 Senior 2 Female
  • 5 Female Senior
  • 6 Female Junior
  • 7 Female Senior
  • 8 Male Senior
  • 9 Male Freshman
  • 10 Female Freshman
  • 11 Male Sophomore
  • 12 Female Sophomore
  • 13 Female Freshman
  • 14 Female Sophomore
  • 15 Male Freshman
  • 16 Male Freshman
  • 17 Female Sophomore
  • 18 Female Junior
  • 19 Female Senior
  • 20 Female Senior
  • 21 Female Junior
  • 22 Male Freshman
  • 23 Female Senior
  • 24 Male Junior
  • 25 Female Junior
  • 26 Male Senior

Questions include identifying variables and levels of measurement, creating pie charts, frequency and probability tables, graphs illustrating distributions, calculating probabilities, conducting significance tests regarding age differences, and estimating proportions and confidence intervals related to loans.

Paper For Above instruction

The analysis of data in business research often involves understanding the types and levels of variables, visualizing distributions, and employing statistical inference to draw conclusions about populations. This study illustrates such applications using a fictitious dataset of college students, covering variables like gender, class level, age, GPA, loan status, and loan balances.

Identification of Variables and Measurement Levels

The first step involves classifying variables based on their nature and measurement levels. Gender is a qualitative nominal variable, indicating categories without inherent order. Class level (Freshman, Sophomore, Junior, Senior) is a qualitative ordinal variable, representing ordered categories. Age and GPA are quantitative interval variables, measurable on a scale with meaningful intervals but no true zero point. Loan status (HasLoans) is a qualitative nominal variable with categories 'Yes' or 'No.' Loan balance is a quantitative ratio variable, with a meaningful zero point and the capacity for ratio comparisons (e.g., twice as much).

Visualizing Variable Distributions

To illustrate the distribution of class levels, a pie chart provides a clear visual, showing proportions of students in each category. Based on the data, a pie chart with appropriate labels and percentages helps stakeholders quickly grasp the composition of the student body. Similarly, bar or column graphs can depict the distribution of gender and class level combined, highlighting subgroup differences. Such visualizations encode categorical data effectively, aiding in descriptive analysis.

Frequency and Probability Tables

Constructing a frequency table for gender and class level involves tabulating the count of students in each category combination. This table summarizes how many students are male or female across class levels, providing foundational insights. Probability tables extend this by calculating the proportion of the total sample that each subgroup represents. For example, the probability that a randomly selected student is a female junior is obtained by dividing the count of female juniors by the total number of students.

Graphical Representation of Bivariate Distributions

To depict the distribution of gender versus class level, a stacked bar chart or grouped column chart is appropriate. This visualization omits total row/column bars, focusing solely on subgroup comparisons. It graphically illustrates intersectional data, such as the proportion of males versus females within each class level, enhancing interpretability for decision-making.

Conditional Probability Calculations

Using the data, several probabilities are computed. For instance, the probability that a randomly selected male student is a freshman is determined by dividing the number of male freshmen by the total number of students. Similarly, conditional probabilities, such as the likelihood of a student being female given that they are a junior, are calculated. These metrics inform targeted strategies, such as resource allocation for specific student groups.

Statistical Inference on Age and Loan Data

Assessing whether male students are older than females involves hypothesis testing. An independent samples t-test compares mean ages; the null hypothesis posits no difference, while the alternative suggests males are older. Conducting this test at both 1% and 10% significance levels determines the robustness of the results. The p-value indicates the probability of observing the data under the null, guiding conclusions about statistical significance.

Similarly, differences in the proportion of students with loans between genders are examined through proportion tests. The null hypothesis assumes equal proportions, with the test determining if observed differences are statistically significant at specified alpha levels. Adjustments in significance level may alter interpretations, emphasizing the importance of context in decision-making.

Estimation of Loan Balance Means and Confidence Intervals

Estimating the average loan balance involves calculating the sample mean of students with loans. Assuming a known population standard deviation, a z-interval computes the 95% confidence interval, encapsulating the true population mean with specified confidence. Furthermore, to achieve a desired margin of error (e.g., $300), sample size calculations use the known standard deviation and the z-value for 95% confidence, guiding data collection efforts.

Conclusion

This comprehensive application of quantitative methods demonstrates how statistical techniques underpin informed business decisions. From classifying variables to hypothesis testing and confidence interval estimation, these tools facilitate understanding and interpreting complex data in an academic or business context. Effective visualization and careful statistical inference empower stakeholders to make evidence-based choices about student demographics, loan programs, and related strategies.

References

  • Agresti, A., & Finlay, B. (2009). Statistical Methods for the Social Sciences (4th ed.). Pearson.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
  • Glen, S. (2018). Understanding Confidence Intervals. Simply Psychology.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W. H. Freeman.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • Sheskin, D. J. (2004). Handbook of Parametric and Nonparametric Statistical Tests. Chapman & Hall/CRC.
  • Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
  • Zimmerman, D. W. (1993). Statistical Power Analysis. Journal of Educational Statistics, 18(2), 151-192.
  • Hahn, G. J., & Meeker, W. Q. (1991). Statistical Intervals: A Guide for Practitioners. Wiley.
  • Salkind, N. J. (2010). Statistics for People Who (Think They) Hate Statistics. Sage.

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