Which statement about parameters in statistical models is true?

Which statement about parameters in statistical models is true?

• A. They are random variables that change with each sample.
• B. They are the actual observed sample values.
• C. They are the means of the sample.
• D. They describe the relations between variables in the population.

Answer: (D)

Parameters are fixed, unknown quantities that define the population model and describe how variables relate to each other in the population. They represent the true, underlying relationships and do not change from one sample to another (what changes is our estimate of them based on data). That’s why describing the relations between variables in the population is the correct statement. It captures that parameters define the population-level model, such as the true regression slope or the population mean. The other ideas describe things we actually observe or compute from data. A value that changes with each sample is a statistic, not a parameter. The actual observed sample values are data, not parameters. The means of the sample are a specific statistic, not the general concept of a population parameter.

Parameters are fixed, unknown quantities that define the population model and describe how variables relate to each other in the population. They represent the true, underlying relationships and do not change from one sample to another (what changes is our estimate of them based on data).

That’s why describing the relations between variables in the population is the correct statement. It captures that parameters define the population-level model, such as the true regression slope or the population mean.

The other ideas describe things we actually observe or compute from data. A value that changes with each sample is a statistic, not a parameter. The actual observed sample values are data, not parameters. The means of the sample are a specific statistic, not the general concept of a population parameter.