Final answer:
Appropriate to assume equal variances between two independent means when one standard deviation of one group is no more than double that of the other group.
Step-by-step explanation:
When dealing with two independent means, it is appropriate to assume equal variances when one standard deviation is no more than double the other.
The relevant part of the question pertains to comparing two population means where population standard deviations are unknown, which can be categorized under independent group means with unknown population standard deviations (10.1 Two Population Means with Unknown Standard Deviations). According to guidelines for this type of analysis, specifically an F test for equality of variances, equal variances can be assumed if the largest sample standard deviation is not more than twice as large as the smaller one.
Thus, the correct option is D) When one standard deviation is no more than double the other. This ensures that the variance between the two groups is not significantly different so that an independent samples t-test can be accurately performed.