if we are testing for the difference between two populations, it is assumed that the two populations are approximately normal and have equal variances, true or false

True.

True. When testing for the difference between two populations, the assumption of approximate normality and equal variances is often made. This assumption is necessary for several statistical tests, such as the independent samples t-test, to be valid.

To determine if the assumption of approximate normality is met, you can check the distributions of both populations using graphical methods like histograms or quantile-quantile (Q-Q) plots. If the data is not strongly skewed or does not have extreme outliers, it is reasonable to assume approximate normality.

To check the assumption of equal variances, you can perform a statistical test called Levene's test or examine the ratio of the variances. If the p-value from Levene's test is greater than the chosen significance level (usually 0.05), or the ratio of the variances is close to 1, then the assumption of equal variances is met.

It is important to note that if these assumptions are not met, there are alternative tests available, such as Welch's t-test, that can handle situations with unequal variances or non-normality.