Cogito
Probability and Statistics · Chapter 8 · Lesson 1
Confidence Intervals
A range, and how sure you are of it.
12 problems · about 22 minutes · TEKS P.S.4.D, S-IC.B.4
What this lesson teaches
The student computes and interprets a confidence interval for a proportion.
- A confidence 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.
Warm Up
Straightforward practice. Get the method working first.
5 problemsEstimate 55% with margin 3. What is the upper end, in percent?
Answer 58
Why 58%.
How does a larger sample change the interval?
Answer It narrows it, since the margin of error shrinks.
Why The interval narrows.
Estimate 45% with margin 4. Upper end, in percent?
Answer 49
Why 45 + 4.
Estimate 30% with margin 5. Lower end?
Answer 25
Why 30 − 5.
Interval 38% to 46%. What is the estimate?
Answer 42
Why The midpoint.
Build It Up
The same ideas with more to keep track of.
3 problemsInterval 38% to 46%. Margin of error?
Answer 4
Why Half the width.
450 of 900 said yes. Sample percentage?
Answer 50
Why 450 ÷ 900.
Quadrupling the sample size does what to the margin? 1 halves it, 2 quarters it.
Answer 1
Why It improves with the square root.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich interpretation of 95% confidence is correct?
Answer About 95% of intervals built this way capture the true value.
Why The confidence describes the method, not one result.
Estimate 72% with margin 6. Lower end?
Answer 66
Why 72 − 6.
The Interval: Estimate 60% with margin 3. What is the lower end, in percent?
Answer 57 %
Why 57%.
The Width: An interval runs from 42% to 50%. What is the margin of error, in percentage points?
Answer 4
Why 4.