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Data ID Sal Compa Mid Age EES SER G Raise Deg Gen1 Gr ..7 0 M E The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? ..9 0 M B Note: to simplify the analysis, we will assume that jobs within each grade comprise equal work. ..6 1 F B ..5 1 M E The column labels in the table mean: ..7 1 M D ID – Employee sample number Sal – Salary in thousands ..5 1 M F Age – Age in years EES – Appraisal rating (Employee evaluation score) ..7 1 F C SER – Years of service G – Gender (0 = male, 1 = female) ..8 1 F A Mid – salary grade midpoint Raise – percent of last raise . M F Grade – job/pay grade Deg (0= BS\BA 1 = MS) ..7 1 F A Gen1 (Male or Female) Compa - salary divided by midpoint, a measure of salary that removes the impact of grade ..8 1 F A ..5 0 M E This data should be treated as a sample of employees taken from a company that has about 1,..7 0 F C employees using a random sampling approach. . F A ..9 1 F A ..7 0 M C Mac Users: The homework in this course assumes students have Windows Excel, and . F E can load the Analysis ToolPak into their version of Excel. ..6 0 F B The analysis toolpak has been removed from Excel for Windows, but a free third-party ..6 1 M A tool that can be used (found on an answers Microsoft site) is: ..8 0 F B ..3 1 M F Like the Microsoft site, I make cannot guarantee the program, but do know that ..8 1 F D Statplus is a respected statistical package. You may use other approaches or tools ..3 0 F A as desired to complete the assignments. ..8 0 F D . M A ..2 0 F A ..9 1 M C ..4 0 F F ..4 0 M F ..3 0 M D ..9 1 F A ..6 0 M B ..5 1 M E ..9 1 M B ..3 0 F A ..3 0 F A ..2 0 F A ..5 0 M E ..5 0 F B ..3 0 M A ..3 0 M C ..7 1 F A ..5 0 F F ..2 1 M E ..2 1 F D ..9 1 M E ..5 1 M E ..3 1 F E ..6 0 M E ..6 0 M E Week 2 Week 2 Testing means with the t-test For questions 2 and 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. 1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries? Males Females Ho: Mean salary = 45 Ho: Mean salary = 45 Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set. t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation Male Ho Female Ho Mean Mean Variance Variance 334. Observations Observations Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 df 24 df 24 t Stat 1. t Stat -1. P(T

Paper For Above instruction

The ongoing debate regarding gender pay equality hinges on whether males and females are compensated equally for performing the same work under similar conditions, as outlined by the Equal Pay Act. Examining this question necessitates rigorous statistical analysis, particularly utilizing hypothesis testing techniques such as the t-test, to compare the salary distributions of male and female employees within a company. The dataset in question, which includes variables such as salary, age, appraisal score, years of service, and gender, provides the foundation for testing whether observed differences reflect actual disparities or are attributable to sampling variability.

First, understanding the structure of the data is crucial. The dataset comprises employee identifiers, salaries (both actual and relative to grades), demographic information like age and gender, and professional metrics such as appraisal ratings and years of service. Salary measures include the raw salary in thousands and a compensated measure that adjusts for grade differences, known as 'compa,' which normalizes salaries relative to grade midpoints.

The primary hypothesis testing framework involves setting null and alternative hypotheses regarding the equality of mean salaries: the null hypothesis (H0) posits that the mean salary for males and females is equal, while the alternative hypothesis (Ha) suggests that the means differ. For example, in the case of comparing the overall sample mean salary of 45 units, one-sided and two-sided t-tests are conducted to assess whether the sample means for males and females significantly deviate from this benchmark.

To determine if males and females in the population are equally paid, one must perform a two-sample t-test assuming unequal variances, given that variances between groups may differ. The test output, including the t-statistic, degrees of freedom, and p-value, guides the decision to reject or fail to reject the null hypothesis at a significance level of 0.05. If the p-value exceeds 0.05, the evidence is insufficient to conclude a salary disparity; if it falls below, the null hypothesis is rejected, indicating a significant difference.

In the data provided, the t-tests indicate that, for the sample, we do not reject the null hypothesis that the average salaries of males and females are equal to 45 units. Moreover, when directly comparing the sample means of male and female salaries, the t-test results suggest no significant difference, implying that, at least from this sample, gender-based pay disparities may not be present. However, the interpretation must consider potential limitations, such as sample size, variability within groups, and whether the sample is representative of the entire population.

Additional information that would be beneficial includes detailed distributional data for salaries within each gender group, information on job roles, tenure, performance ratings, and other factors influencing pay. Such data could account for confounding variables that may obscure true disparities. For instance, differences in experience, position, or performance could explain salary differences that are not directly attributable to gender.

In assessing whether to rely on salary or 'compa' measures, which adjust for grade-related differences, it is more appropriate to analyze the 'compa' scores for a fairer comparison across roles. If the 'compa' measures reveal disparities not apparent in raw salary data, it indicates that gender wage gaps persist even when accounting for job level. Conversely, if 'compa' scores show no difference, it suggests that pay within comparable roles is equitable.

Based on the current analysis, the evidence from the t-tests suggests there is no significant gender pay gap in the sampled data. Nevertheless, this conclusion aligns with the importance of comprehensive data and robust statistical controls. Making broad claims about wage equity requires examining multiple variables and larger samples to ensure biases or confounders are minimized. Ultimately, ensuring equal pay involves ongoing scrutiny and adherence to legal standards, emphasizing transparency and fairness in compensation practices.

References:

1. Blau, F. D., & Kahn, L. M. (2017). The Gender Wage Gap: Extent, Trends, and Explanations. Journal of Economic Literature, 55(3), 789–865.

2. Bureau of Labor Statistics. (2022). The Economics Daily: Highlights of Women’s Earnings in 2021. U.S. Department of Labor.

3. Corbett, C., & Hill, C. (2012). Graduating to a Pay Gap: The Earnings of Women and Men One Year after College Graduation. AAUW.

4. Levinson, M. (2018). The Gender Wage Gap and Equal Pay Legislation. Harvard Law & Policy Review.

5. OECD. (2020). Gender wage gap (indicator). OECD Statistics.

6. OECD. (2023). Paid Parental Leave (indicator). OECD Statistics.

7. Reskin, B. F., & Padavic, I. (2008). Women and Men at Work (2nd ed.). Pine Forge Press.

8. U.S. Equal Employment Opportunity Commission. (2020). Equal Pay and Compensation Discrimination.

9. World Economic Forum. (2022). Global Gender Gap Report 2022.

10. Yellen, J. (2014). Income Inequality and the Wealth Gap. Brookings Institution.