Inferential Statistics • Lesson 8

Confidence Intervals

Learn how to estimate a population parameter using a range of plausible values instead of relying only on a single point estimate.

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Concept 1CONFIDENCE INTERVAL

What Is a Confidence Interval?

A confidence interval gives us a range of values constructed from sample data to estimate an unknown population parameter at a stated confidence level. Unlike a point estimate, it communicates uncertainty caused by sampling variation.

Learn by seeing

From one number to a range

Point Estimate
      ₹2,500

          ↓

Confidence Interval
   ₹2,350 ───── ₹2,650

Point Estimate + Margin of Error
= Confidence Interval

The interval gives decision-makers a range rather than relying only on one sample statistic.

Point Estimate

₹2,500

One value

Confidence Interval

₹2,350–₹2,650

A range

Analyst mindset

Think beyond one number

1. Start with the point estimate

Identify the sample statistic being used as the estimate.

2. Add uncertainty

The margin of error shows how far the interval extends.

3. Consider precision

Sample size and variability affect the width of the interval.

Lesson summary

Remember these ideas

Confidence interval

Estimates a population parameter using a range.

Point estimate

Provides the central numerical estimate.

Margin of error

Determines how far the interval extends from the estimate.

Confidence level

Describes long-run coverage of the procedure.

Larger sample

Generally improves precision.

Greater variability

Generally increases interval width.

95% interpretation

Concerns repeated sampling and long-run coverage.