Final answer:
A confidence interval (CI) is an interval estimate used to approximate the range within which an unknown population parameter lies, considering the desired confidence level, sample size, and other factors. It's often used to make predictions about a population mean or proportion based on sample data. For example, a 95% CI means we're 95% confident that the true population parameter is within this range.
Step-by-step explanation:
The term you are asking about refers to a confidence interval (CI), which is an interval estimate for an unknown population parameter and reflects the uncertainty around the estimate of this parameter.
The CI depends on several factors such as the desired confidence level, known information about the distribution (like the standard deviation), sample size, and the sample itself.
For instance, a 95% confidence interval for a population mean means that if we were to take many samples and build a confidence interval from each of them, about 95 out of 100 of those confidence intervals would contain the true population mean.
Let's take an example where we have a sample mean (x) of 10, and we have constructed a 90 percent CI of (5, 15). This interval was created using a certain margin of error (EBM), which, in this case, is 5.
The EBM is influenced by the confidence level we desire and the characteristics of our sample. Therefore, the CI can be expressed as (x - EBM, x + EBM).
When dealing with qualitative data such as survey responses that measure a proportion, we can also calculate a CI for the true population proportion.
Although the formulas differ slightly, the concept remains the same involving the confidence level, the sample size, and the estimated proportion of successes (p') in the sample.
For example, if we derive a sample proportion of 0.60 or 60%, and the error bound for a population proportion (EBP) is calculated at 0.04, the confidence interval for the true population proportion would be (0.56, 0.64), meaning that we are 90% confident the true proportion lies within this interval.
The complete question is: The numeric distance from the estimated population value in which the true (but unknown) population value may lie with a given probability. Elaborate!