Final answer:
Knowledge of the sampling distribution of a statistic primarily helps researchers understand the variability of the sample statistic. It does not enable the prediction of exact population parameters, elimination of sampling bias, or increase in sample size.
Step-by-step explanation:
Knowledge of the sampling distribution of a statistic enables researchers to a) Understand the variability of the sample statistic. This variability is captured by the standard deviation of the sampling distribution, which can decrease as the sample size increases. While researchers use sample data to make inferences about the population, the exact value of the population parameter is typically unknown and cannot be precisely predicted; hence, option b) is incorrect. Sampling bias is a different issue that arises from the method of sample selection, and knowledge of the sampling distribution does not eliminate it, making option c) incorrect. Lastly, option d), which suggests that knowing the sampling distribution can increase the sample size, is incorrect because the sample size is determined before the sampling distribution can be estimated.Within the context of inferential statistics, sample statistics such as the sample mean (μ) and sample standard deviation (s) are used to estimate population parameters. Confidence intervals are constructed to provide a range of plausible values for the unknown population parameter, reflecting the desired confidence level and incorporating the known information about the sample and its distribution.