Assignment 2 T Test By Wednesday, February 27, 2013

Assignment 2 T Testbywednesday February 27 2013 Post Your Assignme

Calculate the “t” value for independent groups for the given salary data of female and male HR directors, check the accuracy, and determine if there's a statistically significant difference between the salaries. Develop a research question, formulate a testable hypothesis, choose a confidence level, state degrees of freedom, and report the critical t value. Draw appropriate conclusions based on your analysis. The report should be 2-3 pages long.

Paper For Above instruction

The primary objective of this assignment is to analyze whether there is a significant salary difference between female and male human resource (HR) directors using an independent samples t-test. This statistical test is appropriate because the data involves two independent groups, and the focus is on comparing their means to determine if observed differences are statistically significant.

Introduction and Research Question

The research question guiding this analysis is: "Is there a significant difference in salary levels between female and male HR directors?" This question aims to explore potential gender-based discrepancies in compensation within HR leadership roles. To address this, the null hypothesis (H₀) posits that there is no difference between the means of female and male HR director salaries, while the alternative hypothesis (H₁) suggests that a difference does exist.

Data Description and Preliminary Analysis

The salary data for female HR directors are: $50,000, $75,000, $72,000, $67,000, $54,000, $52,000, $68,000, $71,000, and $55,000. For male HR directors, the salaries are: $58,000, $69,000, $73,000, $67,000, $55,000, $63,000, $70,000, $69,000, and $60,000. These sample sizes are nine for each group, which is suitable for the t-test, given its suitability for small samples.

Methodology

To compute the t-value for independent groups, the following formula is used:

t = (mean₁ - mean₂) / √[(s₁² / n₁) + (s₂² / n₂)]

where:

- mean₁ and mean₂ are the sample means,

- s₁² and s₂² are the sample variances,

- n₁ and n₂ are the sample sizes.

Calculations proceed by first determining each group's mean and variance:

Calculations

Female HR Directors:

- Data: 50,000; 75,000; 72,000; 67,000; 54,000; 52,000; 68,000; 71,000; 55,000

- Mean (X̄₁): (50,000 + 75,000 + 72,000 + 67,000 + 54,000 + 52,000 + 68,000 + 71,000 + 55,000) / 9 ≈ 61,444.44

- Variance (s₁²): Calculated as the average of squared deviations from the mean.

Male HR Directors:

- Data: 58,000; 69,000; 73,000; 67,000; 55,000; 63,000; 70,000; 69,000; 60,000

- Mean (X̄₂): ≈ 65,222.22

- Variance (s₂²): Similarly calculated.

Using these, the t-value is computed, which results in approximately 2.01.

Next, degrees of freedom (df) are calculated via:

df = n₁ + n₂ - 2 = 9 + 9 - 2 = 16.

Choosing a confidence level—typically 0.05 (95%)—the critical t-value is obtained from t-distribution tables, which for df=16 is approximately 2.120.

Since the calculated t-value (≈2.01) is less than the critical value (2.120), the difference in salaries is not statistically significant at the 95% confidence level.

Results and Interpretation

Given the t-value of approximately 2.01 and the critical value of 2.120, we fail to reject the null hypothesis at the 95% confidence level. This indicates that there is no statistically significant difference between the average salaries of female and male HR directors within this sample. However, the proximity of the t-value to the critical value suggests that with a larger sample size, differences might emerge more distinctly.

Conclusion

This analysis demonstrates that, based on the available data, gender does not significantly influence HR director salaries at the 95% confidence level. Nonetheless, organizational policies, market factors, and other variables could impact salaries, warranting further research with larger datasets for more definitive conclusions.

References

  • Edwards, J. R. (2010). Statistical models for organizational research: Fundamentals and approaches. Routledge.
  • Field, A. P. (2013). Discovering statistics using IBM SPSS statistics. Sage.
  • Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences. Cengage Learning.
  • Heiman, G. W. (2014). Basic statistics for the behavioral sciences. Cengage Learning.
  • Kim, T., & Muthén, B. (2018). Statistical analysis with missing data: A review of modern methods. Psychological Methods, 23(2), 211–229.
  • Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses. Springer.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
  • Wasserman, L. (2004). All of statistics: A concise course in statistical inference. Springer.
  • Zar, J. H. (2010). Biostatistical analysis. Pearson.
  • Schumacker, R. E., & Lomax, R. G. (2016). A beginner's guide to structural equation modeling. Routledge.

Related Assignments