Suppose that the variable under consideration is normally distributed in each of the two populations and that you are going to use independent simple random samples to compare the population means. Fill in the blank and explain your answer: Unless you are quite sure that they ---------- are equal, the nonpooled $t-$procedures should be used instead of the pooled $t$-procedures.

Unless you are quite sure that they -------- are equal, the non pooled$t-$procedures should be used instead of pooled $t$-procedure.

The variable under consideration is normally distributed across both populations, and the samples are simple random independent.

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 variable under consideration is assumed to be normally distributed in each of the two populations, and the samples are simple random independent.

Following the assumption for pooled and nonpooled $t$procedures, unless you are absolutely certain that the population standard deviations are equal, nonpooled $t$-procedures should be used instead of pooled $t$-procedures.