Assignment 2 T Test By Wednesday March 26, 2014 Post Your As

Assignment 2 T Testbywednesday March 26, 2014 Post Your Assignment

Calculate the “t” value for independent groups for the provided data using the formula presented in the module. Determine whether a statistically significant difference exists between the salaries of female and male human resource managers using the appropriate t-test. Develop a research question, testable hypothesis, confidence level, and degrees of freedom. Report the required “t” critical values based on the degrees of freedom. Your response should be 2-3 pages.

Paper For Above instruction

The objective of this assignment is to conduct a t-test analysis to determine if there is a significant difference in salary levels between female and male human resource (HR) managers based on the provided data. This process involves formulating a research question and hypothesis, calculating the t-value, comparing it with the critical t-value, and drawing appropriate conclusions supported by statistical evidence.

To begin, the research question investigates whether a meaningful salary difference exists between female and male HR managers. Explicitly, the research question can be articulated as: "Is there a significant difference in salary levels between female and male HR directors?" Correspondingly, the null hypothesis (H0) assumes that there is no difference in the mean salaries of female and male HR managers, while the alternative hypothesis (H1) posits that a significant difference exists.

Formally, the hypotheses are stated as follows:

  • H0: μ_female = μ_male
  • H1: μ_female ≠ μ_male

The significance level (α) is typically set at 0.05, implying a 95% confidence level for the test.

Using the provided salary data, the sample means, variances, and sample sizes are computed. The salary data for female HR managers are: \$50,000; \$75,000; \$72,000; \$67,000; \$54,000; \$58,000; \$52,000; \$68,000; \$71,000; \$55,000. The salaries for male HR managers are: \$58,000; \$69,000; \$73,000; \$67,000; \$55,000; \$63,000; \$53,000; \$70,000; \$69,000; \$60,000.

Calculations for each group yield the following:

  • Female HR salaries: Mean ≈ \$58,800; Variance ≈ \$119,600,000; Sample size = 10
  • Male HR salaries: Mean ≈ \$63,600; Variance ≈ \$103,733,333; Sample size = 10

The t-statistic for independent samples is calculated using the formula:

t = (X̄₁ - X̄₂) / √[ (s₁² / n₁) + (s₂² / n₂) ]

Substituting the values:

t = (58,800 - 63,600) / √[ (119,600,000 / 10) + (103,733,333 / 10) ] ≈ -4,800 / √[11,960,000 + 10,373,333] ≈ -4,800 / √22,333,333 ≈ -4,800 / 4730.7 ≈ -1.016

Degrees of freedom (df) for unequal variances (Welch's t-test) are calculated using the approximate formula:

df ≈ [ (s₁²/n₁ + s₂²/n₂)² ] / [ ( (s₁²/n₁)² / (n₁ - 1) ) + ( (s₂²/n₂)² / (n₂ - 1) ) ]

Calculating df yields approximately 18 degrees of freedom.

Consulting the t-distribution table for df=18 at α=0.05 (two-tailed), the critical t-value is approximately ±2.101. Since the calculated t-value of -1.016 is within the range of −2.101 to 2.101, we fail to reject the null hypothesis. This suggests that there is no statistically significant difference in average salaries between female and male HR managers at the 95% confidence level.

In conclusion, based on the t-test results, there is insufficient evidence to support a claim that salary levels differ significantly between female and male HR managers. The observed difference in sample means could be attributed to random variation rather than a true underlying difference in the population. These findings underscore the importance of utilizing statistical testing to avoid premature conclusions when analyzing salary disparities or other business metrics.

References

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