Interpreting Sampling Variability and Margin of Error Quiz

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Quizzes Created: 7252 | Total Attempts: 9,525,313
| Questions: 20 | Updated: Nov 16, 2025
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1) Which of the following is the best point estimate of the population proportion who prefer the library based on the simulations?

Explanation

The best point estimate is the mean of the sample proportions, which is 0.58.

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About This Quiz
Interpreting Sampling Variability And Margin Of Error Quiz - Quiz

This quiz focuses on sampling variability and how it affects estimates. You'll learn how to interpret margin of error in the context of sample data and make informed decisions about sample sizes. By using simulation models, you'll explore how different sample sizes impact the margin of error and how you... see morecan increase accuracy by adjusting your sampling strategy. see less

2)
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2) Using the given margin of error rule, what is the 95% margin of error for the estimate?

Explanation

Margin of error ≈ 2 × 0.035 = 0.070.

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3) Which 95% confidence interval corresponds to the estimate from the simulations?

Explanation

Interval = 0.58 ± 0.07 → (0.51, 0.65).

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4) If a new single sample of 200 students yields 0.62 preferring the library, which statement best explains this result?

Explanation

0.62 is close to 0.58 and within the margin of error.

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5) If the organization doubled the sample size to n=400, what is the most likely impact on the margin of error?

Explanation

A larger sample size usually makes the margin of error smaller.

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6) What is the best point estimate for the population mean daily screen time?

Explanation

The best estimate is the mean of the sample means, 3.9 hours.

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7) What is the approximate 95% margin of error for the mean?

Explanation

Margin of error ≈ 2 × 0.4 = 0.8 hours.

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8) Which 95% confidence interval correctly reflects the estimate?

Explanation

Mean ± margin = 3.9 ± 0.4 → (3.5, 4.3).

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9) If another study reports CI (3.6, 4.2), how does it compare?

Explanation

The intervals overlap, so both estimates are consistent.

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10) If the city wants to cut the margin of error in half, what should they do?

Explanation

MOE is halved by multiplying the sample size by 4.

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11) A survey of 600 adults finds 54% support with ±4% MOE. Interpretation?

Explanation

54% ± 4% → CI of 50% to 58%.

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12) Two candidates: X: 48% ±3%; Y: 51% ±3%. Conclusion?

Explanation

Intervals overlap; race is statistically too close to call.

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13) A school estimates mean books read: 2.8 with CI (2.4, 3.2). Which is correct?

Explanation

The 95% CI refers to long-run capture rate.

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14) A club reports 40% ± 6%. How to reduce sampling variability?

Explanation

Larger random samples reduce sampling variability.

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15) Desired MOE ±2% at 95%: sample size?

Explanation

Using MOE ≈ 1/√n → n ≈ 2500.

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16) Sample n=900 → p̂=0.46, MOE ±3.3%. Smaller MOE?

Explanation

Larger sample reduces MOE.

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17) Sampling variability is:

Explanation

Sampling variability = natural differences across random samples.

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18) Poll: 52% ±3%. Which is NOT justified?

Explanation

95% CI does not mean 95% support.

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19) Poll A (n=400): 60% ±5%; Poll B (n=1600): 58% ±2.5%. Explanation?

Explanation

B’s larger sample size explains smaller MOE.

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20) Simulating samples of n=50 from population mean 70, SD 10:

Explanation

CLT: sample means ~ normal centered at true mean.

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Which of the following is the best point estimate of the population...
Using the given margin of error rule, what is the 95% margin of error...
Which 95% confidence interval corresponds to the estimate from the...
If a new single sample of 200 students yields 0.62 preferring the...
If the organization doubled the sample size to n=400, what is the most...
What is the best point estimate for the population mean daily screen...
What is the approximate 95% margin of error for the mean?
Which 95% confidence interval correctly reflects the estimate?
If another study reports CI (3.6, 4.2), how does it compare?
If the city wants to cut the margin of error in half, what should they...
A survey of 600 adults finds 54% support with ±4% MOE....
Two candidates: X: 48% ±3%; Y: 51% ±3%. Conclusion?
A school estimates mean books read: 2.8 with CI (2.4, 3.2). Which is...
A club reports 40% ± 6%. How to reduce sampling variability?
Desired MOE ±2% at 95%: sample size?
Sample n=900 → p̂=0.46, MOE ±3.3%. Smaller MOE?
Sampling variability is:
Poll: 52% ±3%. Which is NOT justified?
Poll A (n=400): 60% ±5%; Poll B (n=1600): 58% ±2.5%. Explanation?
Simulating samples of n=50 from population mean 70, SD 10:
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