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Inference from sample statistics and margin of error: worksheet with answers

Work through the questions first, then open the answer key and explanations to check your work.

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1
For a poll with sample size 200, the margin of error is 12 percentage points. Assume the margin of error is inversely proportional to the square root of sample size. If the sample size is multiplied by 9, what is the new margin of error, in percentage points?
2
A random sample estimates that 44% of a town’s 1400 adults use its library. The margin of error is 7 percentage points. Using the upper endpoint of this interval, estimate the number of adults who use the library.
3
A random sample estimates that 43% of the students at a large school support a proposal. The margin of error is 6 percentage points. What is the lower endpoint, in percent, of the reported interval?
4
For a poll with sample size 140, the margin of error is 8 percentage points. Assume the margin of error is inversely proportional to the square root of sample size. If the sample size is multiplied by 4, what is the new margin of error, in percentage points?
5
A random sample estimates that 49% of the students at a large school support a proposal. The margin of error is 7 percentage points. What is the lower endpoint, in percent, of the reported interval?
6
For a poll with sample size 260, the margin of error is 16 percentage points. Assume the margin of error is inversely proportional to the square root of sample size. If the sample size is multiplied by 16, what is the new margin of error, in percentage points?
7
A random sample estimates that 47% of a town’s 1700 adults use its library. The margin of error is 5 percentage points. Using the upper endpoint of this interval, estimate the number of adults who use the library.
8
A random sample estimates that 46% of the students at a large school support a proposal. The margin of error is 4 percentage points. What is the lower endpoint, in percent, of the reported interval?
9
A random sample estimates that 58% of the students at a large school support a proposal. The margin of error is 6 percentage points. What is the lower endpoint, in percent, of the reported interval?
10
For a poll with sample size 440, the margin of error is 16 percentage points. Assume the margin of error is inversely proportional to the square root of sample size. If the sample size is multiplied by 16, what is the new margin of error, in percentage points?
11
A random sample estimates that 56% of a town’s 2600 adults use its library. The margin of error is 4 percentage points. Using the upper endpoint of this interval, estimate the number of adults who use the library.
12
A random sample estimates that 55% of the students at a large school support a proposal. The margin of error is 3 percentage points. What is the lower endpoint, in percent, of the reported interval?

Answer key and explanations

1. Answer
4

The square root of sample size is multiplied by 3, so the margin of error is divided by 3: 12/3 = 4 percentage points.

2. Answer
714

The upper percentage is 44 + 7 = 51%. Multiply the population by this proportion: 1400·51/100 = 714.

3. Answer
37

Subtract the margin of error from the estimate: 43 − 6 = 37%. The margin is in percentage points.

4. Answer
4

The square root of sample size is multiplied by 2, so the margin of error is divided by 2: 8/2 = 4 percentage points.

5. Answer
42

Subtract the margin of error from the estimate: 49 − 7 = 42%. The margin is in percentage points.

6. Answer
4

The square root of sample size is multiplied by 4, so the margin of error is divided by 4: 16/4 = 4 percentage points.

7. Answer
884

The upper percentage is 47 + 5 = 52%. Multiply the population by this proportion: 1700·52/100 = 884.

8. Answer
42

Subtract the margin of error from the estimate: 46 − 4 = 42%. The margin is in percentage points.

9. Answer
52

Subtract the margin of error from the estimate: 58 − 6 = 52%. The margin is in percentage points.

10. Answer
4

The square root of sample size is multiplied by 4, so the margin of error is divided by 4: 16/4 = 4 percentage points.

11. Answer
1560

The upper percentage is 56 + 4 = 60%. Multiply the population by this proportion: 2600·60/100 = 1560.

12. Answer
52

Subtract the margin of error from the estimate: 55 − 3 = 52%. The margin is in percentage points.

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