Title: Confidence Intervals | What you need to know for your Six Sigma exam.
Headings: Confidence Intervals
Confidence Intervals
Confidence Interval vs Confidence Level
Confidence Interval vs Prediction Interval
Estimating Population Mean and Standard Deviation
Margin of Error
Z Scores
Common confidence intervals and corresponding Z scores
Confidence Interval Question Using Z-Score
Confidence Interval Question Using T-Score
Calculating the Confidence Interval Comparing Two Population Means
Example
Additional Confidence Intervals Videos
Confidence intervals for Variation
Confidence intervals for Proportion
What are the Difference Between Control Limits and Confidence Intervals?
Confidence Interval
Also See:
Other Confidence Intervals Problems
ASQ Six Sigma Black Belt Exam Confidence Intervals Questions
Authors

Content: Once we find the point estimate, we also need to know how accurate it is. For instance , the Central Limit Theorem says that in a large enough sample group (30 or more), the sample’s mean and standard deviation will be close to those of the population. Margin of Error
Margin of error is the maximum expected difference between the actual population parameter and a sample estimate of the parameter. In other words, it is the range of values above and below sample statistics. Margin of error widely used in surveys tells the degree of uncertainty that the survey results might have. Margin of error = 1/√n
Where n= sample size
Margin of error is the product of critical value and the standard error in the confidence interval. If margin of error increases, confidence level increases. Similarly, margin of error decreases, confidence level also decreases. For example, to estimate confidence interval, we may use X̅±E
E is the margin of error
Confidence interval = X̅±Zα/2*σ/√n
Where σ= population standard deviation
Zα/2= normal distribution value for the desired confidence level
n= sample size
X̅= sample mean
Z Scores
A Z score is the number of standard deviations between a data point and its mean. Thus, you can use a Z-score table to find the corresponding Z-score for common confidence levels, or calculate the α value using this formula: