Title: A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size – Introductory Business Statistics
Headings: 
39 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size
Calculating the Confidence Interval
Changing the Confidence Level or Sample Size
Calculating the Confidence Interval: An Alternative Approach
The confidence interval estimate will have the form:
Calculating the Confidence Interval Using EMB
Finding the z -score for the Stated Confidence Level
Calculating the Error Bound ( EBM)
Constructing the Confidence Interval
Summary: Effect of Changing the Confidence Level
References

Content: The margin of error ( EBM) depends on the confidence level (abbreviated CL ). The confidence level is often considered the probability that the calculated confidence interval estimate will contain the true population parameter. However, it is more accurate to state that the confidence level is the percent of confidence intervals that contain the true population parameter when repeated samples are taken. Most often, it is the choice of the person constructing the confidence interval to choose a confidence level of 90% or higher because that person wants to be reasonably certain of his or her conclusions. There is another probability called alpha ( α ). α is related to the confidence level, CL. α is the probability that the interval does not contain the unknown population parameter. Mathematically, 1 – α = CL. A confidence interval for a population mean with a known standard deviation is based on the fact that the sampling distribution of the sample means follow an approximately normal distribution. Suppose that our sample has a mean of = 10, and we have constructed the 90% confidence interval (5, 15) where EBM = 5.