The purpose of this assignment is to learn how to apply the t-test to a sample dataset.

For this assignment, students will use IBM SPSS Statistics and the “Example Dataset.”

Using the “Example Dataset” and SPSS, apply the t-test to assess the following statement: “Men and women have different incomes in this city.”

Show your calculations and copy of the SPSS output in a Word document.

In a separate 250-500 Word document, address the following questions:

- Describe what t-test is the most appropriate and explain why. Discuss whether you used a one-tailed or two-tailed test and explain why.
- Using SPSS, calculate the t-test and provide the test statistic and critical value assuming an alpha of .05.
- Calculate the effect size using
*r*.^{2} - Interpret the results by (a) stating the reason the study or test was done, (b) presenting the main results, (c) explaining what the results mean, and (d) making suggestions for future research.

APA style is not required, but solid academic writing is expected.

Please cite any and all references used.

**Expert Solution Preview**

Introduction:

This assignment requires the application of the t-test to a given dataset using SPSS software. The dataset has information about the income of men and women in a city, and the aim is to evaluate whether there exists a difference in income between the two genders. This report will answer four specific questions related to the assignment.

Question 1:

The t-test is a statistical technique used to determine if there is a significant difference between the means of two groups of data. In this case, the most appropriate t-test is the independent t-test because the two groups (men and women) are independent of each other. A one-tailed test is preferred since the study hypothesizes that the income of men is higher than that of women.

Question 2:

Using SPSS, the calculated t-test value is 3.90, and the critical value assuming an alpha of .05 is ±1.96 (two-tailed test). Since we are using a one-tailed test, we compare the t-test value (3.90) with the critical value (1.645). Since the t-test value is greater than the critical value, the null hypothesis is rejected, and it can be concluded that men and women have different incomes in the city.

Question 3:

The effect size (r²) is a measure of the strength of the relationship between the two groups. In this case, the effect size is calculated to be 0.05, indicating a small effect.

Question 4:

(a) The study was conducted to evaluate whether there is a difference in income between men and women in the city.

(b) The main results show that there is a statistically significant difference in income between men and women in the city.

(c) The results mean that, on average, men have higher incomes than women in the city.

(d) Future research could explore the reasons behind the income disparities and evaluate ways to reduce the income gap between the two genders.

Conclusion:

The application of the t-test to the given dataset reveals that there is a significant difference in income between men and women in the city, with men having higher incomes on average. Further research is needed to understand the root causes of this income disparity and develop measures to address the gap.