Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances. In order to test the difference between the population means, the test statistic is:

A) a standard normal random variable
B) approximately standard normal random variable
C) Student t-distributed with 58 degrees of freedom
D) Student t-distributed with 33 degrees of freedom
E) Student t-distributed with 18 degrees of freedom

Independent Samples

Samples that are collected from separate populations and are not related or paired in any way, ensuring that the observations are independent of each other.

Normal Populations

Normal populations are groups or sets of entities that have characteristics following a normal distribution, which is symmetric around its mean.

Student T-Distributed

Refers to a family of distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.