Confidence Intervals for a Proportion

An estimate with its uncertainty attached.

11 problems · about 25 minutes · AP Statistics 6.1, 6.3

What this lesson teaches

The student interprets a confidence interval and identifies what changes its width.

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.

Straightforward practice. Get the method working first.

4 problems

Estimate 55%, margin 6%. Lower end as a percent?
Answer 49
Why 49%.
Estimate 40%, margin 5%. Lower end as a percent?
Answer 35
Why 40 − 5.
Estimate 40%, margin 5%. Width of the interval, in percentage points?
Answer 10
Why Twice the margin.
A larger sample makes the interval which? 1 for narrower, 2 for wider.
Answer 1
Why More information.

The same ideas with more to keep track of.

3 problems

Raising confidence from 95% to 99% makes it which? 1 for narrower, 2 for wider.
Answer 2
Why More certainty costs precision.
Select every correct interpretation of a 95% confidence interval.
Answer The method captures the true value in 95% of samples.; The true value is fixed; the interval varies.
Why Confidence describes the procedure across repeated samples.
Interval 49% to 55%. Does it establish a majority? 1 for yes, 0 for no.
Answer 0
Why It contains 50%.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Estimate 70%, margin 2%. Upper end as a percent?
Answer 72
Why 70 + 2.
To halve the margin of error, roughly how many times the sample size is needed?
Answer 4
Why The margin shrinks with the square root of n.
The Lower End: Estimate 60% with margin of error 4%. What is the lower end, as a percent?
Answer 56
Why 56%.
The Upper End: Same interval. What is the upper end, as a percent?
Answer 64
Why 64%.