Practice Margin of Error in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

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% ยฑ\pm 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%95\% MOE is 0.040.04 at n=600n=600. Approximately what MOE do we get at n=2400n = 2400 (other things equal)?

Example 2

hard
A 90%90\% MOE uses zโˆ—=1.645z^* = 1.645. With SE =0.02= 0.02, compute the MOE.

Example 3

hard
A 99% CI for the average household size uses ฯƒ=1.6\sigma=1.6, n=400n=400, and zโˆ—=2.576z^*=2.576. Compute ME to four decimals.

Example 4

medium
A sample of n=400n=400 has p^=0.5\hat{p} = 0.5. Compute the MOE for a 95%95\% CI using zโˆ—=1.96z^* = 1.96.

Example 5

easy
Higher confidence levels make the margin of error ____.

Example 6

medium
A 99%99\% MOE is larger or smaller than a 95%95\% MOE (other things equal)?

Example 7

hard
For a poll with p^=0.10\hat{p}=0.10 vs p^=0.50\hat{p}=0.50 at the same nn and confidence, which has the larger margin of error?

Example 8

easy
With zโˆ—=2z^*=2 and SE =5=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% (zโˆ—=2z^*=2). Using the conservative p^=0.5\hat{p}=0.5 (so SE =0.5/n=0.5/\sqrt{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%95\% CI for a mean is (72,78)(72, 78). What is the point estimate and the MOE?

Example 13

challenge
A poll reports 48% ยฑ\pm 3% for A and 52% ยฑ\pm 3% for B. Can we conclude B leads at 95% confidence? Discuss the overlap.

Example 14

easy
A 95% CI is [10,ย 14][10,\ 14]. What is the margin of error?

Example 15

medium
A study wants a margin of error of 2 with ฯƒ=10\sigma=10 and zโˆ—=2z^*=2. Find the required sample size.

Example 16

easy
MOE has the same units as ____.

Example 17

hard
Two polls each with n=1000n = 1000 report p^1=0.50\hat{p}_1 = 0.50 and p^2=0.46\hat{p}_2 = 0.46. Approximate the SE of the difference (treat p^(1โˆ’p^)\hat{p}(1-\hat{p}) as 0.250.25).

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 ฯƒ\sigma, same confidence), how must nn change?
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