Independent t-test

#1
Alright I've really been struggling with this one so maybe I can find some help here.

If, with the use of the independent t test, the null hypothesis were correct, would the mean value of a variable in one sample be very similar to or different from the mean value for that variable in the other sample?

I thought that the variables would be similar because the null hypothesis on a independent t-test would be that they is no difference between the two sets of data. Am I right on this?
 
#2
Hi,
You and Monty are correct in expecting the sample means to be 'similar' if the null hypothesis is true. This is because the distribution of (xbar-ybar) has a mean of 0 under the null hypothesis.

To clarify what Monty is saying about Ho, the null hypothesis is that the population means, mu1 and mu2 are equal. This hypothesis is either true or not true and has nothing to do with chance.

The chance comes in when we consider the value of the test statistic when we obtain the p-value. This p-value is the probability that the difference in means would be as large, or larger, than that obtained if the null hypothesis is true.

Hope this helps!
:)