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: To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need as an estimate for μ and we need the margin of error. Here, the margin of error ( EBM) is called the error bound for a population mean (abbreviated EBM ). The sample mean is the point estimate of the unknown population mean μ. The confidence interval estimate will have the form: (point estimate – error bound, point estimate + error bound) or, in symbols, ()
The mathematical formula for this confidence interval is: 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 ).