10.33 Regarding the four conditions required for using the pooled $t-$procedures:
a. what are they?
b. how important is each condition?

To find the four conditions required for using the pooled $t-$procedures.

The following assumptions are made for comparing two population means using the pooled $t$ - procedure.
(1) Simple random variables
(2) Independent samples
(3) Normal population or large samples
(4) Equal population standard deviation.

To find that the importance of each condition required for using the pooled $t-$procedures.

The following assumptions are made for comparing two population means using the pooled $t$- procedure.

(1) Simple random variables
(2) Independent samples
(3) Normal population

(4) Equal population standard deviation.
The pooling $t$- test can also be used to compare two means in a specified experiment if assumptions $1$and$2$ are met.
In the case of large samples, the pooled $t$- test is robust to modest violation of assumption$3$ (normal populations).
In the case of nearly equal sample sizes, the pooled $t$- test is robust for moderate violation of assumption $4$(equal population standard deviation).