The width of a confidence interval is the distance between its lower and upper bounds, equal to twice the margin of error. It shrinks when you increase sample size and grows when you raise the confidence level, so a narrower interval means a more precise estimate of the population parameter.
The width of a confidence interval is just upper bound minus lower bound. Since every interval has the form estimate ± margin of error, the width is always twice the margin of error. A narrow interval pins down the parameter tightly. A wide interval tells you the data leaves a lot of uncertainty.
Three things control the width. First, the confidence level. A 99% interval uses a bigger critical value (z*) than a 95% interval, so demanding more confidence costs you a wider interval. Second, sample size. Bigger samples shrink the standard error, which shrinks the width (n sits in the denominator under a square root, so quadrupling the sample only halves the width). Third, variability in the data. For the two-sample z-interval in Topic 6.8, the formula (p̂₁ - p̂₂) ± z* √(p̂₁(1-p̂₁)/n₁ + p̂₂(1-p̂₂)/n₂) shows all three at once. Anything that makes the part after the ± bigger makes the interval wider.
This idea lives in Topic 6.8 (Confidence Intervals for the Difference of Two Proportions) in Unit 6, supporting learning objectives AP Stats 6.8.C and AP Stats 6.8.D, where you calculate the interval and interpret what range of differences is plausible. But it's really an idea about every confidence interval you build in the inference units. The AP exam loves asking 'what happens to the width if...' questions because they test whether you understand the formula instead of just plugging into it. If you can explain why raising the confidence level from 95% to 99% widens the interval, or why one interval containing 0 changes your conclusion about a difference in proportions, you're doing the conceptual reasoning the exam rewards.
Keep studying AP Statistics Unit 6
Margin of Error (Unit 6)
Width and margin of error are the same idea measured differently. The margin of error is the distance from the center to one edge, so the width is exactly two margins of error. Any factor that changes one changes the other.
Confidence Level (Unit 6)
Higher confidence means a bigger critical value z*, which directly stretches the interval. A practice question asks which level guarantees at least 98% of intervals capture the true difference, and the answer (98% or higher) comes with a width cost.
Sample Size (Unit 6)
Sample size is the one lever that narrows the interval without sacrificing confidence. Because n is under a square root in the standard error, you need four times the data to cut the width in half.
Difference in Population Proportions (Unit 6)
For a two-proportion interval, width determines whether 0 is inside the interval. If it is, like the practice interval (-0.12, 0.04), the data can't rule out that the two population proportions are equal.
Multiple-choice questions test this concept two ways. One type gives you a scenario and asks how a change (bigger sample, higher confidence level) affects the width, and the trap answers reverse the relationship. The other type gives you an actual interval, like a 99% interval of (-0.12, 0.04) for a difference in voter support between two districts, and asks what you can conclude. Since that interval contains 0, you can't claim a real difference between the districts. On free-response inference problems, you compute the interval using the Topic 6.8 formula (AP Stats 6.8.C) and then interpret it in context with units (AP Stats 6.8.D). You don't need to memorize the interval formula because you can build it from the standard error formulas on the provided formula sheet, but you do need to explain what the width tells you about precision.
The margin of error is half the width. If your interval is (0.10, 0.30), the width is 0.20 and the margin of error is 0.10. They respond to the same factors in the same direction, so the distinction only matters when a question asks for a specific number. Read carefully whether you're asked for the full width or the ± part.
The width of a confidence interval equals the upper bound minus the lower bound, which is exactly twice the margin of error.
Increasing the confidence level (say, 95% to 99%) increases z* and makes the interval wider, trading precision for confidence.
Increasing the sample size shrinks the standard error and narrows the interval, but because of the square root, you need 4 times the sample to halve the width.
A narrower interval means a more precise estimate of the parameter; a wider interval means more uncertainty.
For a difference of two proportions, check whether 0 falls inside the interval; if it does, the data does not give convincing evidence that the two population proportions differ.
You can reconstruct the two-sample z-interval formula from the standard error formulas on the AP formula sheet, so focus on understanding what drives the width rather than memorizing.
It's the distance between the interval's two endpoints, equal to twice the margin of error. For an interval like (-0.12, 0.04), the width is 0.16, and a smaller width means a more precise estimate.
No, it's the opposite. Going from 95% to 99% confidence uses a larger critical value z*, which widens the interval. To be more confident you've captured the true parameter, you have to cast a wider net.
The margin of error is the ± part, the distance from the point estimate to one edge. The width is the full distance across, so width = 2 × margin of error. Exam questions can ask for either, so check which one you're computing.
Bigger samples make the interval narrower because n is in the denominator of the standard error. Since n sits under a square root, doubling the sample size does NOT halve the width; you'd need 4 times the sample for that.
It means 0 is a plausible value for p₁ - p₂, so the data does not provide convincing evidence that the two population proportions are different. A 99% interval of (-0.12, 0.04) for two voting districts, for example, can't rule out equal support.