Final answer:
Sample size has an inverse relationship with sampling risk and the allowance for sampling risk in statistics. By increasing the sample size, the risk and the degree of error accepted decreases, which improves the accuracy of the results.
Step-by-step explanation:
The student's question pertains to the relationship between sample size, sampling risk, and the allowance for sampling risk. In statistical analysis, sample size has an inverse relationship with both sampling risk and the allowance for sampling risk. Sampling risk refers to the probability that the sample findings might lead to incorrect conclusions about the population from which the sample was drawn. Larger sample size can decrease sampling risk because it more closely models the population, whereas smaller samples may not capture the population characteristics as well.
Allowance for sampling risk is the degree of error statisticians are willing to accept. When a larger sample size is used, the allowance for sampling risk becomes smaller, meaning that the results are more exact and reliable. If statistical power is low, which refers to the probability of correctly rejecting a false null hypothesis, statisticians may increase the sample size to improve power, keeping the significance level (the probability of type I error) constant.
Rules of thumb for sufficient sample sizes have emerged based on statistical literature, providing guidance on how large a sample should be for credible results. The Central Limit Theorem helps statisticians to understand that, with large sample sizes, sample means will be normally distributed, regardless of the population's distribution. This provides a backbone for conducting various types of hypothesis tests.