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: $n_1=20$

$n_2=15$

The given independent sample has

$n_1=20$

$n_2=15$

The independent sample has size, $n_1=20$

$n_2=15$

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.

The data in the above graph is not regularly distributed.