Final answer:
True, the precision of inference is related to sample size and the width of the confidence interval. Larger samples lead to more precise confidence intervals, while higher confidence levels produce wider intervals.
Step-by-step explanation:
True. Precision of inference is indeed related to both the size of the sample and the width of the confidence interval. In terms of the central limit theorem, as we increase the sample size, our sampling distribution of the mean gets closer to a normal distribution, and the corresponding confidence intervals for the mean become more precise.
In fact, increasing the sample size generally leads to a decrease in the error bound, which in turn narrows the confidence interval. This means you get a more precise estimate of the population parameter. On the flip side, a smaller sample size introduces more variability, leading to wider confidence intervals, thereby making our inference less precise.
The confidence level also plays a critical role. Higher confidence levels lead to wider intervals since they aim to cover more of the normal distribution. For example, a 99 percent confidence interval is wider than a 95 percent confidence interval because it seeks to include more of the entire distribution of possible sample means to ensure a higher level of confidence that the true parameter lies within this range.