Calculating and Interpreting Margin of Error Quiz

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| Questions: 20 | Updated: Nov 16, 2025
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1) A random sample of 400 voters shows that 52% support a new policy. The margin of error is ±3%. What is the confidence interval for the true population proportion?

Explanation

52% ± 3% gives 49% to 55%.

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About This Quiz
Calculating And Interpreting Margin Of Error Quiz - Quiz

This quiz provides you with sample data and requires you to calculate margin of error for population estimates. You'll practice interpreting confidence intervals and understanding how the margin of error applies to estimating population parameters, especially for means and proportions.

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2) A survey of 500 students finds that the average time spent on homework is 2.5 hours per night with a margin of error of ±0.4 hours. Which statement is correct?

Explanation

2.5 ± 0.4 gives a likely true mean between 2.1 and 2.9 hours.

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3) A poll of 800 adults finds that 35% prefer online shopping. The margin of error is ±3.5%. What does this margin of error tell us?

Explanation

Margin of error means true percentage likely between 31.5% and 38.5%.

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4) Two surveys estimate the proportion of people who exercise regularly. Survey A has 200 respondents with a margin of error of ±7%. Survey B has 800 respondents. Approximately what is the margin of error for Survey B?

Explanation

Sample size ×4 → MOE halves (7% to 3.5%).

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5) A sample of 625 high school students shows that 68% plan to attend college. If the margin of error is ±4%, what is the lower bound of the confidence interval?

Explanation

68% − 4% = 64%.

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6) What is the 95% confidence interval for the true average amount spent per customer?

Explanation

8.50 ± 0.31 = 8.19 to 8.81.

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7) The shop owner claims the average customer spends $9.00 per visit. Based on the confidence interval, what can we conclude?

Explanation

$9.00 is outside 8.19–8.81.

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8) If the firm wants to reduce the margin of error to approximately ±$0.16 at the same confidence, about how many customers should they sample?

Explanation

To halve MOE, sample size ×4.

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9) Which changes would increase the margin of error?

Explanation

Bigger variability → larger MOE.

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10) Simulation yields proportions 0.42 to 0.58. MOE?

Explanation

0.50 to 0.58 = 0.08.

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11) A random sample of 900 voters shows 48% for Candidate A, MOE ±3.3%. Which statement is most accurate?

Explanation

Interval crosses 50%.

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12) Mean height margin requirement ±1 inch, σ≈3. Sample size?

Explanation

n≈(1.96×3/1)²≈35.

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13) A survey finds 72% social media use, MOE ±2.8%. Upper bound?

Explanation

72 + 2.8 = 74.8%.

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14) Largest MOE?

Explanation

Small n + p near .50.

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15) Simulation midpoint 0.08, interval ends 0.042–0.118. MOE?

Explanation

0.08-0.042=0.038.

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16) Factory claims 5% defective; interval 0.042–0.118. Conclusion?

Explanation

0.05 is inside interval.

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17) Std dev 0.019 of sample proportions represents?

Explanation

It is the standard error.

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18) 58% approval with ±3%. Interpretation?

Explanation

Interval = 55–61.

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19) Two samples: means 75±4, 78±2. Conclusion?

Explanation

Overlap means inconclusive.

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20) Proportion p̂=0.40, n=600. MOE?

Explanation

≈0.039.

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A random sample of 400 voters shows that 52% support a new policy. The...
A survey of 500 students finds that the average time spent on homework...
A poll of 800 adults finds that 35% prefer online shopping. The margin...
Two surveys estimate the proportion of people who exercise regularly....
A sample of 625 high school students shows that 68% plan to attend...
What is the 95% confidence interval for the true average amount spent...
The shop owner claims the average customer spends $9.00 per visit....
If the firm wants to reduce the margin of error to approximately...
Which changes would increase the margin of error?
Simulation yields proportions 0.42 to 0.58. MOE?
A random sample of 900 voters shows 48% for Candidate A, MOE ±3.3%....
Mean height margin requirement ±1 inch, σ≈3. Sample size?
A survey finds 72% social media use, MOE ±2.8%. Upper bound?
Largest MOE?
Simulation midpoint 0.08, interval ends 0.042–0.118. MOE?
Factory claims 5% defective; interval 0.042–0.118. Conclusion?
Std dev 0.019 of sample proportions represents?
58% approval with ±3%. Interpretation?
Two samples: means 75±4, 78±2. Conclusion?
Proportion p̂=0.40, n=600. MOE?
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