Final answer:
A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. The margin of error for a population mean (EBM) depends on the confidence level (CL). The person constructing the confidence interval will choose a confidence level of 90 percent or higher to be reasonably certain of the conclusions.
Step-by-step explanation:
A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose that our sample has a mean of x = 10, and we have constructed the 90 percent confidence interval (5, 15) where the Error Bound for a Population Mean (EBM) = 5.
To construct a confidence interval for a single unknown population mean, µ, where the population standard deviation is known, we need x as an estimate for µ, and we need the margin of error (EBM). The confidence interval estimate will have the form: (point estimate - error bound, point estimate + error bound) or, in symbols, (x − EBM, x+EBM).
The margin of error (EBM) depends on the confidence level (CL). The confidence level is often considered the probability that the calculated confidence interval estimate will contain the true population parameter. The person constructing the confidence interval will choose a confidence level of 90 percent or higher to be reasonably certain of the conclusions.