Sampling Bias, Precision, and Independence: 10 practice questions

Question 1 of 10

Across repeated samples an estimate fluctuates around a shifted value. Which terms describe the fluctuation and the shift?

1. ARandom variation and bias are the same error source; both can always be removed simply by increasing the number of rows from the existing frame.
2. BSampling variation is random change in an estimate across repeated samples, whereas bias is systematic displacement from the target.
3. CBias is random movement across repeated samples and precision is systematic displacement, so a narrow interval diagnoses low bias even under undercoverage.
4. DA smaller standard error proves that the estimator is centered on the target.

Question 2 of 10

In a coolant comparison, treatment is perfectly aligned with production lot. Why is this a systematic sampling problem?

1. AA smaller standard error means the raw observations have little variability.
2. BRandom variation and bias are the same error source; both can always be removed simply by increasing the number of rows from the existing frame.
3. CPrecision concerns random variation in an estimate, whereas systematic sampling error confounds the effect of interest with another explanatory factor.
4. DBias is random movement across repeated samples and precision is systematic displacement, so a narrow interval diagnoses low bias even under undercoverage.

Question 3 of 10

A reported standard error is very small. What does that establish, and what does it leave unresolved?

1. AA smaller standard error proves that the estimator is centered on the target.
2. BTen repeat readings of one item add exactly as much information about between-item variation as one reading from ten independently produced items.
3. CA smaller standard error represents a more precise estimate, but it does not by itself demonstrate low bias.
4. DA smaller standard error means the raw observations have little variability.

Question 4 of 10

A biased online volunteer survey increases from 1,000 to 100,000 responses. Which limitation is not automatically repaired?

1. ARepeated readings never add information of any kind, even about measurement repeatability.
2. BIncreasing independent sample size generally improves precision but does not automatically remove selection or measurement bias.
3. CA smaller standard error proves that the estimator is centered on the target.
4. DA smaller standard error means the raw observations have little variability.

Question 5 of 10

A laboratory measures the same specimen ten times. Why is this not equivalent to ten independently sampled specimens?

1. ARepeated readings never add information of any kind, even about measurement repeatability.
2. BRandomization removes every kind of selection bias and guarantees that the sampled factories represent the complete target population under study.
3. CTen repeat readings of one item add exactly as much information about between-item variation as one reading from ten independently produced items.
4. DIndependent replication adds information about variation; repeated readings of the same unit do not create the same amount of independent information.

Question 6 of 10

Which design factors jointly determine the precision of an estimate?

1. ARepeated readings never add information of any kind, even about measurement repeatability.
2. BRandomization cannot protect against time trends, because treatment order has no connection to systematic measurement drift.
3. CTen repeat readings of one item add exactly as much information about between-item variation as one reading from ten independently produced items.
4. DPrecision depends on inherent variability, measurement error, independent replication, and the efficiency of the sampling scheme.

Question 7 of 10

Treatments would otherwise be applied in a fixed time order. How does randomization help?

1. ARandomization removes every kind of selection bias and guarantees that the sampled factories represent the complete target population under study.
2. BRandomization cannot protect against time trends, because treatment order has no connection to systematic measurement drift.
3. CFifty clustered observations contain the same independent information as fifty separately sampled units, even when observations within each cluster are nearly identical.
4. DRandomization can protect against systematic order effects by preventing treatment or condition from being aligned with time.

Question 8 of 10

Night shifts are rare and more variable than day shifts, but a fixed-size sample must represent both and estimate the overall mean efficiently. Why can stratification help?

1. APositive dependence increases effective sample size above the row count because similar observations confirm one another.
2. BRandomization cannot protect against time trends, because treatment order has no connection to systematic measurement drift.
3. CStratification can improve representation and sampling efficiency when strata capture important, known sources of variation.
4. DRandomization removes every kind of selection bias and guarantees that the sampled factories represent the complete target population under study.

Question 9 of 10

A survey records 50 pupils in each of 10 schools, with positive similarity inside schools, and reports precision as if all 500 rows were independent. What happens to the effective information?

1. APositive dependence within clusters reduces effective information compared with the same number of independent observations.
2. BUse 500 as the independent sample size because every pupil is a different person.
3. CKeep the independent-row standard error because clustering changes only the point estimate.
4. DIncrease effective information above 500 because similar pupils corroborate one another.

Question 10 of 10

A voluntary online poll has 100,000 responses and a tiny standard error, but its frame excludes offline workers and its wording may bias answers. What distinction must the report make?

1. AA defensible report distinguishes accuracy concerns caused by bias from precision concerns caused by random variation.
2. BIt reports only standard error because systematic error is already represented in that number.
3. CRandom variation and bias are the same error source; both can always be removed simply by increasing the number of rows from the existing frame.
4. DA defensible report combines bias and precision into a single accuracy score.