Final answer:
The confidence interval of a correlation coefficient indeed decreases as the sample size increases, reflecting less variability and more precise estimates of the population parameters.
Step-by-step explanation:
The statement that the confidence interval associated with a correlation coefficient decreases as the sample size increases is True. This concept is anchored in statistical theory, particularly the central limit theorem, which suggests that the distribution of sample means approaches a normal distribution as the sample size grows. Consequently, a larger sample size results in a decrease in the standard error of the sample mean, which in turn reduces the width of the confidence interval.
The essential idea is that smaller sample sizes tend to introduce more variability into estimates, requiring a wider interval to capture the true population mean with the same degree of confidence. In contrast, larger samples provide more accurate estimates of population parameters, thus the confidence intervals can be narrower while still maintaining the same confidence level.
Furthermore, as the number of observations increases, the Student's t distribution approaches the standard normal distribution, thereby affecting the computation of confidence intervals in smaller samples.