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: If we chose Z α = 1.96 we are asking for the 95% confidence interval because we are setting the probability that the true mean lies within the range at 0.95. If we set Z α at 1.64 we are asking for the 90% confidence interval because we have set the probability at 0.90. These numbers can be verified by consulting the Standard Normal table. Divide either 0.95 or 0.90 in half and find that probability inside the body of the table. Then read on the top and left margins the number of standard deviations it takes to get this level of probability. 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).