Final answer:
The assumption that is not required when making inferences about the difference between two population means is the equality of population variances. Other assumptions like independence, normality, and random sampling are necessary for this analysis.
Step-by-step explanation:
When conducting inference about the difference between two population means, the assumption that is NOT required is c. Equality of population variances. This is especially the case when we refer to a two-sample t-test that does not assume equal variances, also known as the Welch's t-test. The other assumptions that are required include a. Independence of observations within each sample, b. Normality of the populations being compared, and d. Random sampling from the populations.
It is important to note that there are different types of t-tests, and some versions do require the assumption of equal variances. However, modern statistical approaches allow for the relaxing of this assumption when it is not met.