Imagine that we gave 100 individuals this short experiment and collected the differences between times in the incongruent & congruent condition. You want to know if men and women differed on this time...

The experiment consists of 100 individuals (50 males and females) and their time difference in congruent and incongruent condition is obtained. The objective of the study is to investigate the behaviour gender-wise. In order to perform the hypothesis testing, we provide the null and alternative hypothesis as:
Null Hypothesis: men and women do not differ on this time between conditions.
Alternative Hypothesis: men and women differ on this time between conditions.
Since the problem statement does not define any strict condition, therefore we take complete negation under alternative hypothesis and consider the test to be a 2-tailed test. Moreover, we consider the level of significance to be 5%. Now, in order to determine the test statistic, we observe that a gender-wise comparison needs to be done based on a single independent variable i.e. time. Therefore, we make use of independent sample t-test. A prerequisite for applying t-test is that the data should follow Normal Distribution. This can be claimed obvious as the sample is large (n>30) and henceforth by central limit theorem the Normality can be assumed. Next we...