Final answer:
The statement regarding small sample sizes leading to greater precision in the correlation coefficient is false. In fact, larger sample sizes tend to produce more precise estimates as they approach a normal distribution according to the central limit theorem and reduce sampling error.
Step-by-step explanation:
The statement "The smaller the sample size, the greater the precision that our correlation coefficient will have" is false. In statistics, the precision of the correlation coefficient is influenced by the sample size; however, it is a larger sample size that tends to produce a more precise estimate. The central limit theorem states that the larger the sample, the closer the sampling distribution of the means becomes to a normal distribution, thereby reducing the standard error and increasing precision. Furthermore, small sample sizes result in more variability and therefore less precision in estimating the population's characteristics. Thus, for more accurate results and to reduce sampling error, one should aim for a larger sample size when investigating correlations.