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 get a 90% confidence interval, we must include the central 90% of the probability of the normal distribution. If we include the central 90%, we leave out a total of α = 10% in both tails, or 5% in each tail, of the normal distribution. To capture the central 90%, we must go out 1.645 standard deviations on either side of the calculated sample mean. The value 1.645 is the z -score from a standard normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail. It is important that the standard deviation used must be appropriate for the parameter we are estimating, so in this section we need to use the standard deviation that applies to the sampling distribution for means which we studied with the Central Limit Theorem and is, . Calculating the Confidence Interval Using EMB
To construct a confidence inte