The observed value of a statistic is never exactly equal to the true parameter. Which word completes the sentence: the observed value is ______ equal to the true parameter?

The observed value of a statistic is never exactly equal to the true parameter. Which word completes the sentence: the observed value is ______ equal to the true parameter?

• A. never
• B. always
• C. sometimes
• D. likely

Answer: (A)

A statistic derived from a random sample is a random variable that fluctuates from sample to sample, while the true parameter is fixed. Because of sampling variability, the value you observe in a single sample will almost always differ from the true parameter. The only time you’d see exact equality is if you happened to measure the entire population (a census) or if, by coincidence, the sample happens to land exactly on the parameter value—effectively impossible in typical continuous data scenarios. So the word that best completes the sentence is never, capturing that exact equality is not expected in ordinary sampling.

A statistic derived from a random sample is a random variable that fluctuates from sample to sample, while the true parameter is fixed. Because of sampling variability, the value you observe in a single sample will almost always differ from the true parameter. The only time you’d see exact equality is if you happened to measure the entire population (a census) or if, by coincidence, the sample happens to land exactly on the parameter value—effectively impossible in typical continuous data scenarios. So the word that best completes the sentence is never, capturing that exact equality is not expected in ordinary sampling.