Final answer:
The risk of incorrect acceptance on a smaller population, given the same sample size and precision requirement, is generally higher compared to a larger population, but without more details, it is more accurate to call it indeterminate.
Step-by-step explanation:
When addressing the risk of incorrect acceptance of the null hypothesis (a Type II or ß error) in testing two unequal populations, the size of the population relative to sample size plays a critical role. Given random selection, the same sample size, and the same precision requirement, the risk of incorrect acceptance on the smaller population is generally higher compared to the larger population. This is because the smaller the population, the higher the impact of sample variation on the overall population estimates. However, without additional information about variance, effect size, and other parameters, it would be more accurate to state that the risk relative to the larger population is indeterminate.
In statistical hypothesis testing, a Type II error occurs when a test fails to reject a false null hypothesis. The power of a statistical test (the probability of correctly rejecting a false null hypothesis) is inversely related to the risk of a Type II error.
For both populations, if the sample sizes are small, there is a greater chance for error. It is recommended to have a sufficiently large population — at least 10 or 20 times the size of the sample — to avoid over-sampling and incorrect results. Additionally, the risk of incorrect acceptance can be reduced by increasing the sample size, choosing a randomized sample, or increasing the confidence level by having a larger interval.