Question

what assumptions are made about the populations from which independent random samples are obtained when the t distribution is used to make small-sample inferences concerning the differences in population means?

Answer 1

When making small-sample inferences using the t distribution for population means, assumptions are made about the normality of the populations, their independence, and equality of standard deviations.

Step-by-step explanation:

When making small-sample inferences about the differences in population means using the t distribution, certain assumptions are made:

1. The populations from which the independent random samples are obtained are normally distributed.
2. The two populations are independent of each other.
3. The populations have equal standard deviations (or variances).

These assumptions ensure the validity of the t-test and the accuracy of the inferences made about the population means.