The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the data were obtained. In each case, decide which of the procedures should be applied.

Independent: $n_1=40$

$n_2=45$

The given independent sample has size, $n_1=40$

$n_2=45$

From the given independent sample

$n_1=40$

$n_2=45$

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. The population is sizable.

Now, the data in the given graph is fairly regularly distributed. Furthermore, standard deviations are not equal, and each sample is unique.