91Ó°ÊÓ

The given independent sample

$n_1=25$

$n_2=20$

From the given data

The assumptions for a pooled $t-$test:

1. A basic random sample from two populations will be chosen.

2. The samples chosen are self-contained.

3. The population is roughly normal.

4. The standard deviations of the populations are the same.

The assumptions for a non-pooled $t-$test:

1. A basic random sample from two populations will be chosen.

2. The samples chosen are self-contained.

3. The population is roughly normal.

4. It is not necessary for the standard deviations of populations to be equal.

The assumptions for the paired $t-$test:

1. The chosen sample should be a simple paired sample.

2. The difference is about average.

3. There is a vast population.

Now, the data in the given graph is fairly regularly distributed. Furthermore, not all standard deviations are created equal.