Examining Gender-Based Disparities in Salaries- An Independent Samples T-Test Analysis

Examining Gender-Based Disparities in Salaries- An Independent Samples T-Test Analysis

Based on the provided salary data for male and female employees, we will test whether there are significant differences in the salaries of the employees at the company based on their genders. Assuming that the samples are independent and their variances are not known but assumed to be equal, the calculated mean salaries for the employees are as follows:

The mean salary for male employees = $190,715.46

The mean salary for female employees = $149,313.65

Next, we will perform a two-sample independent t-test to test the claim that employees of both genders have the same mean salary at the company. Let’s set up the null and alternative hypotheses:

Null Hypothesis (H0)

H0: μ_male = μ_female

Alternative Hypothesis (Ha

Ha: μ_male ≠ μ_female

For the hypothesis test, let’s consider a significance level of 0.05. To perform the t-test, we need the pooled standard deviation (Sp), which is calculated as follows:

Sp = √((s_male^2 * (n_male – 1) + s_female^2 * (n_female – 1)) / (n_male + n_female – 2)), where n_male is the number of male employes and n_female is the number of female employees. From the dataset, the number of male employees is 136, while the number of female employees is 89. Therefore, using this information, the pooled variance can be calculated as follows:

Sp = √((97854.110^2 * (136 – 1) + 86129.614^2 * (89 – 1)) / (136 + 89 – 2))

Sp ≈ 93403.36

The test statistic is then calculated as follows:

T-test statistic = (X_male – X_female) / (Sp * √(1/n_male + 1/n_female)), where X_male is the mean salary of the male employees while X_female is the number of female employees.

T-test statistic = (190715.46 – 149313.65) / (93403.36 * √(1/136 + 1/89))

T-test statistic ≈ 3.2511

The t-test statistic value has been determined to be approximately 3.2511. However, to determine whether this result is significant, it can be compared with the critical value for a 0.05 level of significance. The critical test statistic value for a two-tailed test with df = 223 is about ±1.9707, as determined from the t-table. Since the calculated t-test statistic, t = 3.2511, is greater than the critical test statistic t = ±1.9707, the null hypothesis is rejected. Therefore, one can conclude that there is sufficient statistical evidence to conclude that at the 5% significance level, female employees and male employees do not have the same mean salary.

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Click the ‘scenario’ button below to review the topic and then answer the following question:

A downloadable spreadsheet named HR Sample Data was provided in the Assessment Instructions.

Given the salary data in the spreadsheet, show whether you see any significant differences in the salaries based on gender identification. Assume that the samples are independent, and the variances are unknown but assumed equal.

Calculate the mean salary for male employees and the mean salary for female employees (rounded to the dollar). Use a 0.05 significance level to test the claim that male employees and female employees have the same mean salary. Include your critical value, test statistic, and p-value (rounded to two decimal places).