A single estimate is almost certainly a little wrong. An interval reports a range with a stated level of confidence.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The form
Every interval is estimate plus or minus a margin of error.
Sample size
Quadrupling the sample size halves the margin. Precision improves with the square root, which makes it expensive.
What the level means
It describes the method: about 95% of intervals built this way capture the true value.
The common misreading
Saying "there is a 95% chance the true value is in this interval" treats a fixed parameter as random.
Reading a result
A poll at 52% with a margin of 3 has not established a lead, because the interval still contains 50%.
Estimate plus or minus a margin
Every confidence interval has that form. Recognising the common structure means you are learning one idea repeatedly rather than a separate formula for each situation.
What the confidence level describes
95% confidence means 95% of intervals built by this method capture the true value. It describes the procedure across many samples, not the chance for this particular interval.
Confidence against precision
A wider interval is more likely to be right and less informative. A 100% interval covering everything is useless, so choosing a level is a trade rather than a maximisation.
Conditions matter
Random sampling, independence, and a large enough sample. An interval computed where the conditions fail has no guaranteed coverage, however carefully the arithmetic was done.
Step 2: Try It Yourself
Tap and try it out.
55
Step 3: Watch an Example
One step at a time.
Watch Kofi Build an Interval
600 of 1000 people surveyed said yes, with a margin of error of 3 percentage points.
- Step 1
The sample proportion is 600 ÷ 1000 = 60%.
Step 4: Your Turn
Practice makes it stick.
The Interval
Problem 1 of 2
Estimate 60% with margin 3. Lower end, in percent?
%
The Width
Problem 2 of 2
An interval runs from 42% to 50%. What is the margin of error?
Build the Range
1 of 8
Estimate 45% with margin 4. Upper end?
2 of 8
Estimate 30% with margin 5. Lower end?
3 of 8
Interval 38% to 46%. What is the estimate?
4 of 8
Interval 38% to 46%. Margin of error?
5 of 8
450 of 900 said yes. Sample percentage?
6 of 8
Quadrupling the sample size does what to the margin? 1 halves it, 2 quarters it.
7 of 8
Which interpretation of 95% confidence is correct?
8 of 8
Estimate 72% with margin 6. Lower end?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Estimate 55% with margin 3. Upper end, in percent?
Question 2 of 2
A poll reports 52% with a margin of 3. Has a lead been established?
What You Learned
- An interval is an estimate plus or minus a margin of error.
- Larger samples give smaller margins, improving with the square root.
- The confidence level describes the method, not one particular interval.