Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer below. Select all that apply. A. Sample median used to estimate a population median. B. Sample mean used to estimate a population mean. C. Sample variance used to estimate a population variance. D. Sample proportion used to estimate a population proportion. E. Sample range used to estimate a population range. F. Sample standard deviation used to estimate a population standard deviation.

Question

Mathematics

Naima Sweeney

21 May, 15:50

Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer below. Select all that apply. A. Sample median used to estimate a population median. B. Sample mean used to estimate a population mean. C. Sample variance used to estimate a population variance. D. Sample proportion used to estimate a population proportion. E. Sample range used to estimate a population range. F. Sample standard deviation used to estimate a population standard deviation.

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Answers (1)

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Madelynn · Answer 1

B. Sample mean used to estimate a population mean.

C. Sample variance used to estimate a population variance.

D. Sample proportion used to estimate a population proportion.

Step-by-step explanation:

This is because the mean of the sampling distribution of the mean tends to target the population mean. Also, the mean of the sampling distribution of the variance tends to target the population variance.

This means that the sample mean and variance tend to target the population mean and variance, respectively, instead of systematically tending to underestimate or overestimate that value. This is why sample means and variances are good estimators of population means and variances, respectively. This is also true for proportions but not true for medians, ranges and standard deviations.