The sample varianceA) is always smaller than the true value of the population variance.B) is always larger than the true value of the population variance.C) could be smaller, equal to, or larger than the true value of the population variance.D) can never be zero.

Question

The sample varianceA)  is always smaller than the true value of the population variance.B)  is always larger than the true value of the population variance.C)  could be smaller, equal to, or larger than the true value of the population variance.D)  can never be zero.

Frances Rangel · Accepted Answer

Final Answer : C, Explanation :  The sample variance could be smaller, equal to, or larger than the true value of the population variance. This is because the sample variance is calculated using a subset of the population and therefore may not fully capture the variability of the entire population. However, as the sample size increases, the sample variance tends to approach the true value of the population variance. It is also possible for the sample variance to be equal to the population variance if the entire population is used as the sample. The other options (A, B, D) are incorrect statements.

The sample variance

A) is always smaller than the true value of the population variance.
B) is always larger than the true value of the population variance.
C) could be smaller, equal to, or larger than the true value of the population variance.
D) can never be zero.

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