Sampling error is inevitable because

Sampling error is inevitable because

• A. The population never changes from sample to sample.
• B. The sample size is always equal to the population size.
• C. Sampling eliminates all bias.
• D. The sample may not perfectly represent the population due to random variability.

Answer: (D)

The idea being tested is that using a sample to learn about a population comes with differences that arise purely from random chance. When you select a subset, which individuals end up in that sample is determined by luck, so the statistic you calculate from the sample (like a mean or proportion) will typically not match the true population value exactly. This difference is sampling error, and it is inevitable whenever you rely on a sample rather than observing every member of the population. If you repeated the study with many different random samples, you would see a range of results, and the spread of those results reflects the sampling error. A census, where you measure everyone in the population, would have no sampling error because it isn’t approximating—it's exact with respect to the population. The other statements mix up ideas: sampling error comes from random variability in who is included in the sample, not from the population staying the same; and bias is a separate issue from this random variation. Larger sample sizes reduce sampling error, but they don’t eliminate it completely.

The idea being tested is that using a sample to learn about a population comes with differences that arise purely from random chance. When you select a subset, which individuals end up in that sample is determined by luck, so the statistic you calculate from the sample (like a mean or proportion) will typically not match the true population value exactly. This difference is sampling error, and it is inevitable whenever you rely on a sample rather than observing every member of the population. If you repeated the study with many different random samples, you would see a range of results, and the spread of those results reflects the sampling error. A census, where you measure everyone in the population, would have no sampling error because it isn’t approximating—it's exact with respect to the population. The other statements mix up ideas: sampling error comes from random variability in who is included in the sample, not from the population staying the same; and bias is a separate issue from this random variation. Larger sample sizes reduce sampling error, but they don’t eliminate it completely.