Margin of Error Factors Quiz (HSS.IC.A.1)

1) A polling company increases the sample size from 400 to 1,600 for a proportion estimate at the same confidence level. What happens to the margin of error?

It doubles

It stays the same

It increases by 1.5 times

It halves

Increasing sample size by 4 makes the margin of error about half as big.

Explanation

Increasing sample size by 4 makes the margin of error about half as big.

2) For a fixed sample size, increasing the confidence level from 90% to 99% will do what to the margin of error for a proportion?

Decrease it

Increase it

Keep it unchanged

Make it zero

Higher confidence level → larger margin of error.

Explanation

Higher confidence level → larger margin of error.

3) Which design choice most directly reduces margin of error for an estimate of a population mean?

Increase the sample size

Use a convenience sample

Use a lower-quality instrument

Increase the population size

A bigger sample size reduces margin of error.

Explanation

A bigger sample size reduces margin of error.

4) When estimating a proportion with p near 0.5, how does margin of error compare to when p is near 0.1, holding all else equal?

Larger near 0.5

Smaller near 0.5

The same

Undefined near 0.1

Margin of error is largest when p is close to 0.5.

Explanation

Margin of error is largest when p is close to 0.5.

5) A study doubles the confidence level’s critical z-value. What must be true about the margin of error, assuming standard error is fixed?

It doubles

It halves

It becomes zero

It stays the same

Margin of error = critical value × standard error, so it doubles.

Explanation

Margin of error = critical value × standard error, so it doubles.

6) Which sampling method most likely yields a smaller margin of error for the same sample size?

Voluntary response sampling

Simple random sampling

Judgment sampling

Haphazard sampling

Simple random sampling reduces error more than biased methods.

Explanation

Simple random sampling reduces error more than biased methods.

7) Margin of error most closely depends on which of the following?

Population size and response rate

Standard error and critical value

Survey topic and wording

Sampling frame and cost

Margin of error comes from standard error and the critical value.

Explanation

Margin of error comes from standard error and the critical value.

8) For estimating a mean with known standard deviation, which change will decrease the margin of error?

Decrease the confidence level

Increase the confidence level

Increase the population size

Use fewer decimals

Lower confidence → smaller margin of error.

Explanation

Lower confidence → smaller margin of error.

9) A survey of 1,000 adults has a margin of error of ±3% at 95% confidence. If only 250 adults were surveyed, the margin of error would be approximately:

±1.5%

±9%

±6%

±12%

Sample size goes down by 4, so margin of error doubles → about ±6%.

Explanation

Sample size goes down by 4, so margin of error doubles → about ±6%.

10) In practice, using stratified random sampling (with proportional strata) instead of simple random sampling can reduce margin of error primarily by:

Increasing the critical value

Reducing variability within strata

Increasing population size

Increasing nonresponse

Stratified sampling lowers variability, which reduces margin of error.

Explanation

Stratified sampling lowers variability, which reduces margin of error.

11) Which design has the smallest margin of error?

Design A

Design D

Design B

Design C

Design B has a large sample size and no design effect.

Explanation

Design B has a large sample size and no design effect.

12) Comparing Design B and Design C, what is the main reason Design C’s margin of error is larger?

Smaller sample size

Lower population variability

Different sampling frame

Higher confidence level

Higher confidence level means a bigger margin of error.

Explanation

Higher confidence level means a bigger margin of error.

13) Compared to Design B, Design D’s margin of error is larger primarily because:

Lower confidence level

Higher sample proportion

Design effect inflates standard error

Smaller sample size

Cluster sampling increases standard error due to the design effect.

Explanation

Cluster sampling increases standard error due to the design effect.

14) If the team wants a margin of error about ±2% at 95% confidence using SRS, which change is most appropriate?

Increase n to around 2,400–2,500

Decrease n to 200

Switch to cluster sampling with same n

Increase confidence level to 99%

A sample size near 2,400 is needed for about ±2% margin of error.

Explanation

A sample size near 2,400 is needed for about ±2% margin of error.

15) Which statement about margin of error is true?

It guarantees the sample statistic is within the interval of the true parameter

It quantifies expected sampling variation at a specified confidence level

It measures nonresponse bias directly

It decreases when variability increases

Margin of error tells how much sample results may vary from sampling alone.

Explanation

Margin of error tells how much sample results may vary from sampling alone.

16) For fixed n and confidence level, which situation yields the largest margin of error for a proportion estimate?

P = 0.05

P = 0.20

P = 0.50

P = 0.80

The margin of error is largest when p = 0.50.

Explanation

The margin of error is largest when p = 0.50.

17) A researcher wants to halve the margin of error for a mean estimate (σ known). Approximately how should the sample size change?

Multiply n by 1.5

Multiply n by 2

Multiply n by 4

Multiply n by 8

To cut MOE in half, the sample size must be multiplied by 4.

Explanation

To cut MOE in half, the sample size must be multiplied by 4.

18) Which action typically reduces both margin of error and potential bias?

Raising confidence level

Improving sampling frame and increasing n

Using convenience sampling with larger n

Reducing measurement precision

Better sampling + larger sample both reduce error and bias.

Explanation

Better sampling + larger sample both reduce error and bias.

19) If the standard deviation in the population doubles while n and confidence level stay the same, what happens to the margin of error for a mean?

It stays the same

It halves

It becomes zero

It doubles

Margin of error increases when variability increases.

Explanation

Margin of error increases when variability increases.

20) A school district estimates the proportion of students meeting a benchmark. Which plan best minimizes the margin of error for the same resources?

One large cluster from a single school

Stratify by school, then SRS within each stratum

Use voluntary online responses

Reduce sample size but raise confidence level

Stratified sampling ensures representation and reduces variability.

Explanation

Stratified sampling ensures representation and reduces variability.

Factors Affecting Margin of Error Quiz