Confidence Interval Calculator: Lower Bound & Upper Bound
Introduction & Importance
Confidence intervals are crucial in statistics as they provide a range of values within which we can be confident that the true population parameter lies. The lower and upper bounds of this interval give us a sense of the precision of our estimate.
How to Use This Calculator
- Enter your sample size, confidence level, mean, and standard deviation.
- Click the ‘Calculate’ button.
- View the results below the calculator.
Formula & Methodology
The formula for calculating the confidence interval is:
CI = Mean ± (Z * (Standard Deviation / √Sample Size))
Where Z is the Z-score corresponding to the desired confidence level.
Real-World Examples
Case Study 1: Poll Results
Suppose a poll of 100 voters finds that 60% support a new policy. The standard deviation is 5%.
Case Study 2: Quality Control
A quality control check on a production line finds that 2% of products are defective. The standard deviation is 1%.
Case Study 3: Customer Satisfaction
A customer satisfaction survey finds that 85% of customers are satisfied. The standard deviation is 3%.
Data & Statistics
| Confidence Level | Z-score |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
| Sample Size | Standard Deviation | Lower Bound | Upper Bound |
|---|---|---|---|
| 100 | 5 | 54.8 | 65.2 |
| 1000 | 5 | 59.4 | 60.6 |
| 10000 | 5 | 59.94 | 60.06 |
Expert Tips
- Larger sample sizes result in narrower confidence intervals.
- Increasing the confidence level also increases the width of the interval.
- Confidence intervals are not the same as prediction intervals.
Interactive FAQ
What is a confidence interval?
A confidence interval is a range of values that is likely to contain an unknown population parameter, such as a mean.
What does the confidence level mean?
The confidence level is the probability that the true population parameter lies within the calculated confidence interval.
How do I interpret the confidence interval?
If we calculate a 95% confidence interval, we can be 95% confident that the true population parameter lies within the calculated range.
BLS Guide to Confidence Intervals
Nature: Confidence intervals for the difference between two means
Statistics How To: Confidence Intervals