Final answer:
The robustness of the two-sample t-test refers to the test's ability to produce valid results even when certain statistical assumptions are not perfectly met, specifically the normality assumption, provided the sample sizes are sufficiently large.
Step-by-step explanation:
The robustness of the two-sample t procedure for comparing the means of two populations refers to its ability to provide valid results even when certain conditions are not met. Specifically, the two-sample t-test is robust to violations of the assumption of normality, especially when the sample sizes are large. According to the Central Limit Theorem, if a sample size is sufficiently large, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution.
Furthermore, the ability to compare two means with the two-sample t-test is not severely impacted by the underlying population distributions, particularly when sample sizes are equal or the variances are similar. In practice, the two-sample t-test is frequently used when the population standard deviations are unknown. Sample standard deviations are then used as an estimate for the population standard deviations.
It is also worth noting that the t-test for two independent groups can be applied with the normal approximation to the Student's-t distribution when the total sample size is greater than 30, as stated in Solution 10.7. This suggests that the t-test retains a high level of accuracy even under less-than-ideal conditions, illustrating its robustness.