91Ó°ÊÓ

To explain the use of pooled $t$- test and pooled $t$- interval test is reasonable with the given sample data.

${\overline{x}}_1=39.04,s_1=18.82,n_1=51$

${\overline{x}}_2=49.92,s_2=18.97,n_2=53$

For comparing two population means, the following assumptions are applied when using the pooled $t$-test and pooled $t$-interval test.
(1) Simple random variables
(2) Independent samples
(3) Normal population or large samples.

In the case of large samples, this pooled $t$ - test is robust to moderate violation.
(4) Equal population standard deviation.

In the case of nearly equal sample sizes, this pooled $t$ - test is robust for modest violation.
Assumptions $1$and $3$ are correct based on the data provided.
Also, both populations are regularly distributed, and the sample sizes are large and relatively equal $(n_1=51,n_2=53)$, confirming assumption $3$.
The standard deviations of two populations, $s_1=18.82$and $s_2=18.97$, are close enough to consider assumption $4$met.
Hence, it is reasonable to use pooled $t$- test and pooled $t$- interval test for comparing given two population means.

As a result, it is reasonable, because the sample standard deviations are close to being equal. It is reasonable to assume that the population standard deviations are equal.