Title: 8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size - Introductory Business Statistics | OpenStax
Headings: 8.1
A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size

8.1 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 EBM
Finding the z -score for the Stated Confidence Level
Calculating the Error Bound ( EBM)
Constructing the Confidence Interval
Example 8.1
Solution 1
Interpretation
Example 8.2
Solution 1
Comparing the results
Summary: Effect of Changing the Confidence Level
Example 8.3
Solution 1
Solution 2
Summary: Effect of Changing the Sample Size
Example 8.4
Solution 1

Content: In reality, we can set whatever level of confidence we desire simply by changing the Z α value in the formula. It is the analyst's choice. Common convention in Economics and most social sciences sets confidence intervals at either 90, 95, or 99 percent levels. Levels less than 90% are considered of little value. The level of confidence of a particular interval estimate is called by (1-α). A good way to see the development of a confidence interval is to graphically depict the solution to a problem requesting a confidence interval. This is presented in Figure 8.2 for the example in the introduction concerning the number of downloads from iTunes. That case was for a 95% confidence interval, but other levels of confidence could have just as easily been chosen depending on the need of the analyst. However, the level of confidence MUST be pre-set and not subject to revision as a result of the calculations. Figure 8.2
For this example, let's say we know that the actual population mean number of iTunes downloads is 2.1.