Which of the following statements is correct about a parameter or a statistic associated with repeated random samples of the same size from the same population?

Question

BlackTom AI · Accepted Answer

A parameter is a fixed value that describes a characteristic of a population, such as the population mean or variance. It does not change from sample to sample because it is a property of the entire population. In contrast, a statistic is a value calculated from a sample, such as the sample mean or sample variance, and it can vary from sample to sample. This variability is described by the sampling distribution of the statistic, which is the probability distribution of the statistic over all possible samples of a given size from the population.

- Option a is incorrect because a parameter does not vary from sample to sample; it is fixed for a given population.
- Option b is correct because the values of a statistic do vary according to the sampling distribution for that statistic, reflecting the variability inherent in sampling.
- Option c is incorrect because a parameter does not have a sampling distribution; it is a constant value.
- Option d is incorrect because it incorrectly states that parameters vary from sample to sample, which they do not, and that statistics do not vary, which they do.

Therefore, the correct statement is that the values of a statistic will vary according to the sampling distribution for that statistic.

Which of the following statements is correct about a parameter or a statistic associated with repeated random samples of the same size from the same population?单项选择题

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