Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling

Key principle of test selection:
Whenever the population standard deviation $\sigma$ is KNOWN, the sampling distribution of $\bar{X}$ is normal with standard error $\sigma / \sqrt{n}$, and the test statistic is $Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \sim N(0, 1)$.
It is a Z-test irrespective of sample size $n$ (even when $n = 16 \lt 30$), because normality of sample mean holds and $\sigma$ does not need to be estimated from sample variance.
Student's t-test would only be used if $\sigma$ were unknown.

Analysis of statistical error definitions:

• Correct: The difference between a sample statistic (an estimate) and the corresponding true population parameter arises due to studying a sample rather than the entire population; this difference is specifically termed 'Sampling error'.
• Incorrect: Random error refers to unpredictable variations during experimental trials or measurement noise.
• Incorrect: 'Probability error' is not a standard statistical terminology used for estimator difference.
• Incorrect: Non-sampling error arises from non-response, measurement flaws, recording errors, or faulty questionnaire design, present even in complete census.

Analysis of sampling techniques:

• Incorrect: Purposive (judgmental) sampling involves deliberate selection of subjects based on specific predefined characteristics.
• Incorrect: Snowball sampling relies on existing participants recruiting future participants from among their acquaintances.
• Incorrect: Random sampling ensures every member of the target population has a known, non-zero probability of selection.
• Correct: Convenience (accidental or grab) sampling involves drawing participants simply because they are easily accessible and convenient to recruit, such as passersby at a shopping mall.

Analysis of sampling terminology:

• Correct: A sampling frame (or frame) is a comprehensive list, register, or map containing every individual sampling unit within the target population from which a sample is drawn.
• Incorrect: A cluster is an intact, natural grouping of heterogeneous units treated as a sampling unit.
• Incorrect: Strata are mutually exclusive homogeneous subpopulations formed in stratified sampling.
• Incorrect: Sub-population refers to any subset of the target population.