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Given Size is $n=75$

The following are the assumptions for the pooled$t-$test:

1. A simple random sample was drawn from two populations

2. The samples chosen are distinct.

3. The population is roughly normal.

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

The following are the assumptions for the non-pooled $t-$test:

1. A simple random sample was drawn from two populations

2. The samples chosen are distinct.

3. The population is roughly normal.

4. Population standard deviations do not have to be equal.

The following are the assumptions for the paired role="math" localid="1651302637556" $t$-test:

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

2. The difference is about normal.

3. There is a large population.

Now, the data in the given figure is roughly normally distributed. Furthermore, the population size is 75, which is substantial, and there is no outlier.

As a result, all of the conditions of the paired $t$-test were met. As a result, the paired$t-$test should be used.