Standard Error of the Mean (SEM):
- The standard error of the mean (SEM) measures the variation or dispersion of the sample means around the population mean.
- It quantifies the precision or accuracy of the sample mean as an estimate of the population mean.
- The formula for SEM is given by SEM = standard deviation / √(sample size).

Standard Error of the Mean for Finite Population:
- When the population size is finite, the standard error of the mean for a finite population takes into account the effect of the population size on the sampling process.
- The formula for SEM for a finite population is given by SEM = standard deviation / √(sample size) * √(N - n) / √(N - 1), where N is the population size and n is the sample size.
- The term √(N - n) / √(N - 1) is known as the finite population correction factor.
- The finite population correction factor adjusts for the decrease in variability when sampling from a finite population compared to an infinite population.

Standard Error of the Mean for Infinite Population:
- When the population size is infinite, the standard error of the mean for an infinite population does not consider the effect of the population size on the sampling process.
- The formula for SEM for an infinite population is given by SEM = standard deviation / √(sample size).
- In this case, there is no need for a finite population correction factor since the population size is assumed to be infinite.

Effect of Sampling Fraction on Standard Error of the Mean:
- The sampling fraction is the ratio of the sample size to the population size (n / N).
- When the sampling fraction is small, it means that the sample size is small relative to the population size.
- In this case, the finite population correction factor (√(N - n) / √(N - 1)) becomes close to 1, as the difference between N and n becomes negligible compared to N.
- As a result, the standard error of the mean for a finite population becomes very close to the standard error of the mean for an infinite population.
- This is because the effect of the finite population correction factor diminishes as the sampling fraction decreases.
- Therefore, the correct answer is option 'A' - small sampling fraction.