Final answer:
The statement is true; larger sample sizes are needed to detect differences within variable groups in a population and to reduce sampling variability, producing more reliable results.
Step-by-step explanation:
True. The statement that larger samples are needed to detect real differences between groups within a population is correct. In the field of statistics, particularly when discussing the central limit theorem, it's noted that the larger the sample size, the closer the sampling distribution of the mean will align with a normal distribution. This is important for reducing sampling variability and getting more accurate, representative results.
When considering samples with greater variability within a population, larger sample sizes are indeed necessary. This is because they reduce the effect of outliers and allow for a better estimation of the true population parameters. For instance, in a heterogeneous population where there is high within-group variability, small samples might not capture the full range of the variability, which can lead to incorrect conclusions about the population as a whole.
Therefore, as the variability within the groups of a population increases, if we want to maintain statistical power and control the type II error rate, it's crucial to increase the sample size. This helps in producing more reliable and generalizable results and understanding the true nature of the population being studied.