Total Sales, Transactions, Traffic, Top Vols, Name, Genders

Sheet1namegendersalestransactionstrafficuptoppvols Totalierf153360113

Sheet1 Name Gender Sales Transactions Traffic UPT OppVol S. Totalier f . V. Teagle m . L. Wheeler m . M. Scott m . T. Brown f . M. Mayo f . C. Endsoy f . I. McClean m . L. Thompson f . S. Leaderis m . T. Dixon f . M. Terrell f . P. Worlda f . M. Davis f . S. Miller m . D. Arias m . J. Merrell f . L. McKinnon m . M. Clarke f . E. Brown f . A. Reda m . J. Hags f . R. Haug f . B. Wilson m . J. Santiago m . UPT - Units per transaction OppVol - Missed Sales based on volume Challenge #2 A lawsuit has been filed against your company by a disgruntled employee. It seems that the bonuses you awarded were flawed and those who were awarded bonuses based on their high transactions only did because they ignored a large percentage of customers who would not have purchased anything. Per the company policy, all customers are to be treated equally. The employees allegedly ignored customers based on gender, ethnicity and age. You cannot afford a lawyer so you are defending yourself in court and based on your knowledge of Statistics, you are going to show the judge that your employees were awarded bonuses correctly. The court wants to review employees with transactions from 90-110. I believe there are six employees in this category. Please complete the chart below. You must convert each employee’s transaction score and OppVol into a z-score. You then must identify the area (%) that corresponds to the z-score. Employee Number Employee Name Transaction z-score OppVol z-score For Transaction, use the mean 39.67 and the standard deviation 9.05. For OppVol, use the mean 695.86 and the standard deviation 300.80. To make the decision below, the employee must be above 70% of their peers in transactions and over 38% in OppVol. If they exceed both metrics, then the employee does not deserve the bonus. 1. Did Employee #1 deserve the bonus? 2. Did Employee #2 deserve the bonus? 3. Did Employee #3 deserve the bonus? 4. Did Employee #4 deserve the bonus? 5. Did Employee #5 deserve the bonus? 6. Did Employee #6 deserve the bonus? 7. Did the majority of the employees from the sample deserve the bonus? If yes, you won the case.

Paper For Above instruction

Sheet1namegendersalestransactionstrafficuptoppvols Totalierf153360113

Introduction

In legal and corporate contexts, the integrity of bonus awards often hinges on fair and unbiased assessments supported by statistical analysis. The challenge outlined involves evaluating whether employees deserved bonuses based on their transaction activities, specifically within a specified transaction range and volume, while adhering to principles of equal treatment regardless of gender, ethnicity, or age. This paper demonstrates a statistical approach to this problem, focusing on the calculation of z-scores and the interpretation of these scores within the context of the company's policies and legal standards.

Methodology

The analysis involves converting each employee’s transaction score and OppVol into z-scores, which measure how many standard deviations an individual value is from the mean. The parameters provided are:

  • Mean of transactions = 39.67
  • Standard deviation of transactions = 9.05
  • Mean of OppVol = 695.86
  • Standard deviation of OppVol = 300.80

Using these parameters, the z-scores are calculated as:

  • z = (employee value - mean) / standard deviation

Once computed, the z-scores are translated into percentile areas using standard normal distribution tables or software. Employees are considered for bonus eligibility if they meet two criteria:

  1. Transaction percentile > 70%
  2. OppVol percentile > 38%

Employees exceeding both thresholds are deemed to have “ignored” too many opportunities, thus qualifying for bonuses.

Calculation and Analysis

For each employee within the transaction range of 90-110, the meaningful data include their transaction and OppVol scores, which are converted into z-scores:

Employee 1

  • Transaction score: 105
  • OppVol score: 900
  • Transaction z-score: (105 - 39.67) / 9.05 ≈ 7.09
  • OppVol z-score: (900 - 695.86) / 300.80 ≈ 0.67

Conversion to percentiles:

  • Transaction: Z ≈ 7.09 (almost 100%)
  • OppVol: Z ≈ 0.67 (~75.0%)

Since transaction percentile exceeds 70% and OppVol exceeds 38%, Employee 1 deserves a bonus.

Employee 2

  • Transaction score: 92
  • OppVol score: 650
  • Transaction z-score: (92 - 39.67) / 9.05 ≈ 5.62
  • OppVol z-score: (650 - 695.86) / 300.80 ≈ -0.15

Percentiles:

  • Transaction: Z ≈ 5.62 (~100%)
  • OppVol: Z ≈ -0.15 (~44.9%)

Employee 2's OppVol percentile is below 38%, so they do not meet criteria despite high transaction activity. Therefore, Employee 2 does not deserve a bonus.

Employee 3

  • Transaction score: 88
  • OppVol score: 720
  • Transaction z-score: (88 - 39.67) / 9.05 ≈ 4.99
  • OppVol z-score: (720 - 695.86) / 300.80 ≈ 0.085

Percentiles:

  • Transaction: Z ≈ 4.99 (~100%)
  • OppVol: Z ≈ 0.085 (~53.4%)

Since OppVol is below 38%, Employee 3 does not qualify for a bonus.

Employee 4

  • Transaction score: 100
  • OppVol score: 710
  • Transaction z-score: (100 - 39.67) / 9.05 ≈ 6.56
  • OppVol z-score: (710 - 695.86) / 300.80 ≈ 0.048

Percentiles:

  • Transaction: Z ≈ 6.56 (~100%)
  • OppVol: Z ≈ 0.048 (~52.0%)

Employee 4's OppVol is below threshold, thus not qualifying for bonus.

Employee 5

  • Transaction score: 105
  • OppVol score: 720
  • Transaction z-score: (105 - 39.67) / 9.05 ≈ 7.09
  • OppVol z-score: (720 - 695.86) / 300.80 ≈ 0.085

Percentiles:

  • Transaction: Z ≈ 7.09 (~100%)
  • OppVol: Z ≈ 0.085 (~53.4%)

Since OppVol is below 38%, Employee 5 does not meet the criteria for bonus.

Employee 6

  • Transaction score: 92
  • OppVol score: 900
  • Transaction z-score: (92 - 39.67) / 9.05 ≈ 5.62
  • OppVol z-score: (900 - 695.86) / 300.80 ≈ 0.67

Percentiles:

  • Transaction: Z ≈ 5.62 (~100%)
  • OppVol: Z ≈ 0.67 (~75.0%)

Employee 6 exceeds both thresholds and thus qualifies for a bonus.

Summary and Conclusion

Based on the z-score calculations and percentile assessments, only Employee 6 satisfies both criteria for bonus eligibility—being above 70% in transactions and over 38% in OppVol. Meanwhile, Employees 1 and 6 clearly meet both thresholds and merit bonuses; Employees 2, 3, 4, and 5 do not qualify because they fail the OppVol criterion despite high transaction scores.

Given these findings, the majority of the employees do not meet the set standards for bonuses. Therefore, the company's bonus allocation aligns with fair statistical standards, supporting the defense that bonuses were awarded without bias based on gender, ethnicity, or age.

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