Final answer:
The variability among item values in a population that affects sample size is measured using the standard deviation. Sampling variability of a statistic like the mean is measured by its standard error. Larger sample sizes lead to smaller sampling variability and more precise population parameter estimates.
Step-by-step explanation:
One factor that influences sample size in mean-per-unit estimation is the estimated variability among item values in the population. This variability is measured using the standard deviation. The standard deviation provides a numerical measure of the overall amount of variation in a data set. It is calculated as the square root of the variance, where the variance is the average, or mean, of the squared deviations of each data point from the data set's mean.
When discussing the sampling variability of a statistic, such as the mean, we refer to how much the statistic varies from one sample to another within a population. A key measure of sampling variability is the standard error, which is the standard deviation of the sampling distribution and can be represented as σ/√n, where σ is the population standard deviation and n is the sample size. Hence, the larger the sample size, the smaller the sampling variability or the standard error will be, leading to more precise estimates of population parameters.
Moreover, the variance within samples, an estimate of σ² that is the average of the sample variances, also known as pooled variance, provides useful information about the distribution of data within and between samples. In cases where sample sizes differ, the variance within samples is weighted accordingly. As sample size increases, the estimations for the population standard deviation become more accurate, reducing the confidence interval range needed to capture the true population mean.