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: 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. The sample sized, , shows up in the denominator of the standard deviation of the sampling distribution. As the sample size increases, the standard deviation of the sampling distribution decreases and thus the width of the confidence interval, while holding constant the level of confidence. This relationship was demonstrated in (Figure). Again we see the importance of having large samples for our analysis although we then face a second constraint, the cost of gathering data. Calculating the Confidence Interval: