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: You wish to be very confident so you report an interval between 9.8 years and 29.8 years. This interval would certainly contain the true population mean and have a very high confidence level. However, it hardly qualifies as meaningful. The very best confidence interval is narrow while having high confidence. There is a natural tension between these two goals. The higher the level of confidence the wider the confidence interval as the case of the students’ ages above. We can see this tension in the equation for the confidence interval. The confidence interval will increase in width as increases, increases as the level of confidence increases. There is a tradeoff between the level of confidence and the width of the interval. Now let’s look at the formula again and we see that the sample size also plays an important role in the width of the confidence interval.