The margin of error is the maximum expected difference between a sample statistic and the true population parameter, typically expressed as a plus-or-minus value. It equals half the width of a confidence interval and decreases as sample size increases.
When a poll says '52% ± 3%,' that 3% is the margin of error. It means the true value is probably within 3 percentage points of 52%, so between 49% and 55%.
Showing a random 20 of 76 problems.
Example 1
medium
A 95% MOE is 0.04 at n=600. Approximately what MOE do we get at n=2400 (other things equal)?
Example 2
hard
A 90% MOE uses z∗=1.645. With SE =0.02, compute the MOE.
Example 3
hard
A 99% CI for the average household size uses σ=1.6, n=400, and z∗=2.576. Compute ME to four decimals.
Example 4
medium
A sample of n=400 has p^=0.5. Compute the MOE for a 95% CI using z∗=1.96.
Example 5
easy
Higher confidence levels make the margin of error ____.
Example 6
medium
A 99% MOE is larger or smaller than a 95% MOE (other things equal)?
Example 7
hard
For a poll with p^=0.10 vs p^=0.50 at the same n and confidence, which has the larger margin of error?
Example 8
easy
With z∗=2 and SE =5, compute the margin of error.
Example 9
medium
An election poll gives candidate A 51% with margin of error 4%. Can we confidently say A leads?
Example 10
challenge
A poll needs a margin of error of at most 3 percentage points at 95% (z∗=2). Using the conservative p^=0.5 (so SE =0.5/n), find the minimum sample size.
Example 11
hard
How does quadrupling the sample size affect the margin of error?
Example 12
medium
A 95% CI for a mean is (72,78). What is the point estimate and the MOE?
Example 13
challenge
A poll reports 48% ± 3% for A and 52% ± 3% for B. Can we conclude B leads at 95% confidence? Discuss the overlap.A: [45%, 51%] and B: [49%, 55%] — overlapping intervals; no winner confirmed
Example 14
easy
A 95% CI is [10,14]. What is the margin of error?
Example 15
medium
A study wants a margin of error of 2 with σ=10 and z∗=2. Find the required sample size.
Example 16
easy
MOE has the same units as ____.
Example 17
hard
Two polls each with n=1000 report p^1=0.50 and p^2=0.46. Approximate the SE of the difference (treat p^(1−p^) as 0.25).
Example 18
medium
Doubling the sample size changes the margin by what factor?
Example 19
medium
The MOE captures sampling error only; it does NOT include ____ error.
Example 20
medium
To shrink ME by a factor of 3 (same σ, same confidence), how must n change?