Independent Samples T-Test

The independent samples t-test makes the following assumptions:

• Assumption of Independence: There must be two data sets that are not connected with each other, and are therefore independent.  
• Assumption of Homogeneity of Variance: The variances of the dependent variable must be equal. 
• Assumption of Normality: The sampling distribution of the mean across samples must be normal and therefore must fit the bell curve. The dependent variable must, therefore, be (approximately) normally distributed and must be measured on a continuous scale.

Generally, the null hypothesis for an independent samples t-test is that the two populations are equal. Therefore;

 H0:u1=u2

However, researchers are normally trying to reject the null hypothesis and accept the alternative hypothesis, which states that the population means are not equal;

 H0:u1u2

In order to reject or accept the alternative hypothesis, we must set a significance level known as alpha (). The value of alpha is usually set at 0.o5. 

Your p-value indicates the probability that your null hypothesis is true. If your p-value is less than your selected alpha level, the null hypothesis is rejected and the alternative hypothesis is accepted. However, if your p-value is more than your selected alpha level, the null hypothesis is accepted and the alternative hypothesis is rejected.