Question: The t distribution tells you the probability that the difference you observe is due to chance is the null hypothesis is true. The t-test is a ratio of a statistic over a measure of variability.

Using the t distribution to test a hypothesis is very similar to using the normal distribution. The null hypothesis is that the two populations have the same mean, and thus any difference between the two sample means is due to chance.

The t distribution tells you the probability that the difference you observe is due to chance if the null hypothesis is true. You simply establish a Type 1 error level, and if your observed difference is less probable than the Type 1 error level, reject the null hypothesis and conclude that the two means came from populations with different means.

Calculate the t score for the following Independent-Samples t-test data set.

Self-esteem scores for a challenge course research study
Experimental Group (X1) Control Group (X2)
74 39
52 51
48 68
39 79
62 49
57 49
40 43