Explanation:
Systematic sampling is a type of probability sampling method in which every kth element in the population is selected for inclusion in the sample. The sample size in systematic sampling depends on the interval k.

Factors affecting the sample size in systematic sampling:
- The interval k: The sample size in systematic sampling is directly related to the interval k. If the interval k is small, then the sample size will be larger as more elements from the population will be included in the sample. Conversely, if the interval k is large, the sample size will be smaller.
- The total population size: While the total population size does play a role in determining the sample size in systematic sampling, it is not the primary factor. The interval k is the key determinant of the sample size, as it dictates how many elements will be included in the sample.
- The number of strata: Systematic sampling can also involve stratification, where the population is divided into homogeneous subgroups or strata. The number of strata can impact the sample size, but the interval k within each stratum is still the primary factor influencing the sample size.
- The variance within strata: Variance within strata can affect the precision of the estimates obtained from systematic sampling. Higher variance within strata may require a larger sample size to achieve the desired level of precision.
In conclusion, the sample size in systematic sampling primarily depends on the interval k, as it determines how many elements from the population will be included in the sample. Other factors such as the total population size, number of strata, and variance within strata can also play a role in determining the sample size, but the interval k is the key factor.