Given below are two statements: Statement I: When selection procedure is…
2023
Given below are two statements:
Statement I: When selection procedure is biased, taking a large sample will help reduce the bias.
Statement II: In normally distributed data, the chances of individual observed values deviating more than 3 times the standard deviation from the mean value are very low.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer: D. Statement I is incorrect but Statement II is correct — ConceptRandom sampling error and systematic selection bias are different. Increasing the sample size reduces standard error, approximately in proportion to 1…
- A.
Both Statement I and Statement II are correct
- B.
Both Statement I and Statement II are incorrect
- C.
Statement I is correct but Statement II is incorrect
- D.
Statement I is incorrect but Statement II is correct
Show answer & explanation
Correct answer: D
Concept
Random sampling error and systematic selection bias are different. Increasing the sample size reduces standard error, approximately in proportion to 1 divided by the square root of n, but it does not repair a biased selection mechanism. For a standard normal variable Z, about 99.73% of the probability lies within three standard deviations of the mean.
Application
Statement I concerns systematic selection bias. A larger sample can make a biased estimate more precise, but the same biased selection procedure continues to over-represent or under-represent parts of the population; therefore Statement I is incorrect.
Statement II concerns the normal distribution. Since P(|Z| ≤ 3) is approximately 0.9973, the probability outside this interval is about 1 − 0.9973 = 0.0027, or 0.27%; therefore such deviations are very rare and Statement II is correct.
Combining the two evaluations gives: Statement I is incorrect but Statement II is correct.
Contrast
Both Statement I and Statement II are correct: this treats sample-size growth as a remedy for systematic selection bias.
Both Statement I and Statement II are incorrect: this treats the small normal probability beyond three standard deviations as appreciable.
Statement I is correct but Statement II is incorrect: both evaluations reverse the relevant statistical principles.
Statement I is incorrect but Statement II is correct: this is the combination produced by the bias principle and the three-sigma probability.
Cross-check
Increasing n changes the variability of an estimator, not the population-selection rule. Independently, the standard normal tail calculation gives 2 × P(Z > 3) ≈ 2 × 0.00135 = 0.0027, confirming that observations beyond three standard deviations are uncommon.
Result: Statement I is incorrect but Statement II is correct.