91Ó°ÊÓ

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

${\stackrel{¯}{x}}_1=118,s_1=12.04,n_1=99$

${\overline{x}}_2=110,s_2=11.25,n_2=80$

For comparing two population means, the following assumptions are made 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 $2$ are correct based on the information provided.
Because both populations are regularly distributed and the sample sizes are high $(n_1=99,n_2=80)$, assumption $3$ is likewise confirmed.
The standard deviations of two populations,$s_1=12.04$and $s_2=11.25$, are close enough to consider assumption $4$met.
As a result, pooled $t$- test and pooled $t$- interval test are reasonable for comparing two population means.

Hence, 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.