Final answer:
The amount of uncertainty of a sample estimate is known as the sampling variability of a statistic, quantified using the standard error. A confidence interval uses the sample mean and the margin of error to estimate the range in which the true population parameter lies.
Step-by-step explanation:
The amount of uncertainty of a sample estimate, like a mean or proportion, of a population is known as the sampling variability of a statistic. This variability is often quantified using the standard error, which represents the standard deviation of the sampling distribution, and indicates the precision of the sample estimate as a predictor of the population parameter. When constructing a confidence interval (CI) for an unknown population mean, where the population standard deviation is known, the sample mean (μ) is used along with the margin of error (error bound for a population mean, EBM) to calculate the interval that likely contains the true population parameter.
To construct the CI, you need the sample mean (x) as a point estimate for μ, and the EBM. The CI has the form (point estimate - error bound, point estimate + error bound), or in symbols, (x − EBM, x + EBM). The EBM is dependent on factors such as the desired confidence level, information that is known about the distribution, such as the known standard deviation, and the sample size.