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The population standard deviations are $23.6$and $25.2$ and each sample size is $25$.

The following are the assumptions of the pooled $t$test: - The sample should be a simple random sampling from two populations.

- Each sample is distinct from the others.

- The population is roughly normal.

- Population standard deviations are the same.

The non-pooled $t$ assumption is that the chosen sample should be a simple random sampling from two populations.

- The samples are unrelated to each other.

- The population is rather normal.

- The sample size is substantial.

The two standard deviations' values are not identical in the present case, despite their magnitude being equal.

For non-pooled $t$ tests, this is the assumption.

As a result, for the current circumstance, a non-pooled $t$ test should be utilised.