Any Conclusion Drawn For The T Test Statistical Process

Question

Any Conclusion Drawn For The T Test Statistical Process Is Only As Goo Any conclusion drawn for the t-test statistical process is only as good as the research question asked and the null hypothesis formulated. T-tests are used to compare two sample groups, either on a pre-post test basis or between two independent or dependent samples. The t-test is particularly suitable for small sample sizes, which are common in managerial research. However, when sample sizes become very large, the mathematical calculations involved can become complex and less practical. In this context, we are asked to calculate the “t” value for independent groups using the provided salary data of female and male HR directors. Additionally, we need to assess whether there is a statistically significant difference in salaries between female and male HR managers, formulate the relevant research question and hypothesis, determine the confidence level, degrees of freedom, and compare the calculated “t” value to the critical value. Finally, we must draw appropriate conclusions based on our analysis. The salary data provided includes salaries for female HR directors and male HR directors: - Female HR Directors: $50,000; $75,000; $72,000; $67,000; $54,000; $58,000; $52,000; $68,000; $71,000; $55,000 - Male HR Directors: $58,000; $69,000; $73,000; $67,000; $55,000; $63,000; $53,000; $70,000; $69,000; $60,000 ---

Dr. Jack HW Helper · Accepted Answer

Introduction The gender wage discrepancy in human resource management positions has long been a topic of research and debate. In this analysis, we focus specifically on assessing whether there exists a statistically significant difference in salary levels between female and male HR directors. The core of this investigation is to perform an independent samples t-test, examining whether salary means differ significantly between the two groups, based on the data provided. The research question guiding this inquiry is: "Is there a significant difference in the average salaries of female and male HR directors?" Research Hypotheses and Significance Level The null hypothesis (H₀): There is no significant difference between the mean salaries of female and male HR directors. The alternative hypothesis (H₁): There is a significant difference between the mean salaries of female and male HR directors. The significance level (α) is set at 0.05, which is standard in social science research, indicating a 5% risk of rejecting the null hypothesis when it is actually true. Data Description and Calculation of Descriptive Statistics The provided salary data consists of ten observations for each group. - Female HR Directors: 10 observations - Male HR Directors: 10 observations First, we compute the mean and standard deviation for each group. Female HR Directors: - Salaries: $50,000; $75,000; $72,000; $67,000; $54,000; $58,000; $52,000; $68,000; $71,000; $55,000 Sum of salaries = $50,000 + $75,000 + $72,000 + $67,000 + $54,000 + $58,000 + $52,000 + $68,000 + $71,000 + $55,000 = $652,000 Mean = $652,000 / 10 = $65,200 Calculating the standard deviation (s₁): s₁ = √[(∑(xᵢ - mean)²) / (n - 1)] Similarly, for male HR directors: - Salaries: $58,000; $69,000; $73,000; $67,000; $55,000; $63,000; $53,000; $70,000; $69,000; $60,000 Sum = $58,000 + $69,000 + $73,000 + $67,000 + $55,000 + $63,000 + $53,000 + $70,000 + $69,000 + $60,000 = $637,000 Mean = $637,000 / 10 = $63,700 Standard deviation ca

Any Conclusion Drawn For The T Test Statistical Process Is Only As Goo

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