Final answer:
Yes, a small sample size usually results in a sampling error because the odds are low that a small group can represent the entire population. Larger samples and randomized sampling methods help reduce sampling error and bias, making statistical results more reliable.
Step-by-step explanation:
When considering whether a small sample size usually results in sampling error, it is indeed more likely due to several factors. One such reason is because the odds are low that a small number of participants will accurately represent an entire population. This lack of representativeness can introduce variation or chance error, because a smaller sample is less likely to embody the full range of traits found in the whole population. Statistical analysis and establishing a truly representative sample is complex, and while smaller samples might be necessary in some research scenarios, like rare conditions or crash testing, they are often more susceptible to error.
To reduce sampling error and enhance the reliability of results, it is essential to use larger sample sizes if possible. This ensures a greater chance that the sample will closely approximate the population and thus yield more accurate results. Moreover, employing randomized sampling methods (like simple random sampling or stratified sampling) ensures that each individual in the population has an equal chance of being selected, thereby mitigating bias which can also distort study findings.
In summary, option 2 of the student's provided choices best captures the influence of small sample size on sampling error—'Yes, because odds are low that a few participants will represent an entire population.'