A confidence interval is a point estimate plus and minus a margin of error.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
What 95% confidence means
The method captures the true value in 95% of samples. It is a property of the procedure, not of one interval.
The common misreading
It does not say there is a 95% chance the true value lies in this interval. The true value is fixed; the interval is what varies.
What changes the width
A larger sample narrows it; higher confidence widens it. You cannot have both for free.
Estimate plus or minus a margin
Every confidence interval has the form statistic ± (critical value)(standard error). Recognising that structure means you are learning one idea repeatedly rather than a new formula each time.
What 95% confidence means
The confidence level describes the procedure: 95% of intervals built this way capture the true parameter. It does not mean there is a 95% chance the parameter is in this particular interval.
Conditions must be checked
Random sample, independence via the 10% condition, and large counts — at least 10 successes and 10 failures. The exam awards marks for checking these and deducts for omitting them.
What changes the width
Higher confidence widens the interval; larger samples narrow it, by a factor of the square root of n. Quartering the margin of error requires sixteen times the sample, which is why precision is expensive.
Step 2: Try It Yourself
Tap and try it out.
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Step 3: Watch an Example
One step at a time.
Watch Rosa Read an Interval
A poll reports 52% with a margin of error of 3%.
- Step 1
The interval runs from 49% to 55%.
Step 4: Your Turn
Practice makes it stick.
The Lower End
Problem 1 of 2
Estimate 60% with margin of error 4%. What is the lower end, as a percent?
The Upper End
Problem 2 of 2
Same interval. What is the upper end, as a percent?
Reading Intervals
1 of 8
Estimate 40%, margin 5%. Lower end as a percent?
2 of 8
Estimate 40%, margin 5%. Width of the interval, in percentage points?
3 of 8
A larger sample makes the interval which? 1 for narrower, 2 for wider.
4 of 8
Raising confidence from 95% to 99% makes it which? 1 for narrower, 2 for wider.
5 of 8
Select every correct interpretation of a 95% confidence interval.
6 of 8
Interval 49% to 55%. Does it establish a majority? 1 for yes, 0 for no.
7 of 8
Estimate 70%, margin 2%. Upper end as a percent?
8 of 8
To halve the margin of error, roughly how many times the sample size is needed?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Estimate 55%, margin 6%. Lower end as a percent?
What You Learned
- A confidence interval is an estimate plus and minus a margin of error.
- Confidence is a property of the method across repeated samples, not of one interval.
- Bigger samples narrow it; higher confidence widens it.