Warm-up
Three quick questions from earlier lessons.
Discover
A poll reports 52% support, "plus or minus 3 points". Which range of values is plausible for the true support?
- 49% to 55%
- 52% to 55%
Key idea
An interval estimate: point estimate ± margin of error.
A confidence interval is , with margin of error . The point estimate is the center of the interval; the margin of error is half its width. Larger samples give smaller margins.
Worked example
Interval (0.42, 0.50).
Point estimate
Center.
Margin of error
Half the width.
Written as estimate ± ME.
Your turn, guided
Your turn: interval (12, 20). The margin of error.
(20 − 12)/2.
Practice ★
- A 95% confidence interval for a proportion is (39/100, 49/100). Find the margin of error.
- A 95% confidence interval for a proportion is (20/100, 32/100). Find the margin of error.
- A confidence interval for a mean is (41, 55). Find the point estimate.
Watch out!
Practice ★★
- A 95% interval from a sample of 591 is too wide. Which change makes it narrower?
- A larger sample size
- A higher confidence level, such as 99%
- Nothing: the width is fixed by the population
Exit ticket
Three questions to check you have got it.
- A 95% confidence interval for a proportion is (39/100, 49/100). Find the margin of error.
- A 95% confidence interval for a proportion is (20/100, 32/100). Find the margin of error.
- A 95% confidence interval for a proportion is (27/100, 37/100). Find the margin of error.
Summary card
Interval estimates
Estimate ± ME, ME = critical value × SE; ME = half the width.
Watch out: width = 2 × ME.
End of the lesson
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