A sales sampling frame systematically excludes a relevant part of the target market. What is the principal risk?
Correct Answer
D) Coverage bias not cured by more sales from the frame
Systematically excluding a relevant group creates a coverage problem and can bias estimates if that group differs on the target characteristic. Increasing the number of observations from the same incomplete frame does not automatically fix the omission. Bias and random precision are distinct; an excluded group could coincidentally share the same mean, so a bias of nonzero magnitude is not logically guaranteed for every statistic.
Why This Is the Correct Answer
Option D is correct because systematically excluding a relevant group creates a coverage problem that can bias estimates if that group differs on the characteristic being measured. Adding more observations from the same incomplete frame does not automatically correct that omission.
Why the Other Options Are Wrong
Option A: Wider confidence intervals caused only by a small sample
Option A points to wider confidence intervals caused only by a small sample, but that is a precision issue. The described problem is systematic exclusion, which larger samples from the same frame do not cure.
Option B: Arithmetic errors in calculating the summary statistics
Option B points to arithmetic errors in calculating the statistics, but the problem lies in which sales are included, not in the calculations. Correct arithmetic on a biased frame still gives biased results.
Option C: A breach of client confidentiality in the data set
Option C points to a breach of client confidentiality, which has nothing to do with excluding part of the market from a sampling frame.
Bigger net, same hole
Casting a bigger net with the same hole still misses the same fish; more sales from a flawed frame keep the same gap.
How to use: Use this to remember that sample size does not fix coverage bias.
Exam Tip
When a question describes systematic exclusion, think bias rather than precision.
Common Mistakes to Avoid
- -Believing more data from the same frame removes bias
- -Confusing bias with random sampling error
- -Treating coverage problems as calculation errors
Concept Deep Dive
Analysis
This question tests the difference between bias and random error in sampling. When a sampling frame systematically omits part of the target market, the problem is coverage, which can bias results if the omitted group differs. Collecting more sales from the same incomplete frame does not fix the omission.
Background Knowledge
A sampling frame is the list from which observations are drawn. If it leaves out part of the population, results can be biased toward the included portion. Bias and random sampling error are distinct: more data reduces random error but does not repair a flawed frame.
Real-World Application
An appraiser pulls sales only from the MLS, missing builder-direct sales of new homes in the area. Adding more MLS sales does not fill that gap, so she researches builder sales separately.
More Statistics Questions
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