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: This is what was called in the introduction, the "level of ignorance admitted". Changing the Confidence Level or Sample Size
Here again is the formula for a confidence interval for an unknown population mean assuming we know the population standard deviation: X - − Z α ( σ n) ≤ μ ≤ X - + Z α ( σ n)
X - − Z α ( σ n) ≤ μ ≤ X - + Z α ( σ n)
It is clear that the confidence interval is driven by two things, the chosen level of confidence,
Z α
Z α, and the standard deviation of the sampling distribution. The Standard deviation of the sampling distribution is further affected by two things, the standard deviation of the population and the sample size we chose for our data. Here we wish to examine the effects of each of the choices we have made on the calculated confidence interval, the confidence level and the sample size. For a moment we should ask just what we desire in a confidence interval. Our goal was to estimate the population mean from a sample. We have forsaken the hope that we will ever find the true population mean, and population standard deviation for that matter, for any case except where we have an extremely small population and the cost of gathering the data of interest is very small. In all other cases we must rely on samples. With the Central Limit Theorem we have the tools to provide a meaningful confidence interval with a given level of confidence, meaning a known probability of being wrong.