Asked by Melisa Baranli on Sep 29, 2024
Verified
Which of the following statements is true?
A) The sample mean is relatively more efficient than the sample median.
B) The version of the sample variance where you divide by n is biased.
C) The sample mean is consistent.
D) All of these choices are true.
Sample Mean
is the average value of a subset of observations from a larger population.
Sample Variance
Sample variance is a measure of the dispersion or variability of a sample dataset, calculating how much the numbers differ from the sample mean.
Consistent
A statistical property indicating that as the size of the sample increases, the estimator converges in probability to the parameter being estimated.
- Comprehend the impact of sample size in enhancing the reliability of estimations.
- Discern the defining characteristics of adept estimators, embodying unbiasedness, consistency, and relative efficiency.
- Specify the benchmarks for making choices among alternative estimators.
Verified Answer
HR
Hunter Radfordabout 4 hours ago
Final Answer :
D
Explanation :
All the statements provided are true. The sample mean is more efficient than the sample median under normal distribution due to lower variance. The version of the sample variance where you divide by n (instead of n-1) is biased because it tends to underestimate the population variance. The sample mean is consistent, meaning it converges in probability to the true population mean as the sample size increases.
Learning Objectives
- Comprehend the impact of sample size in enhancing the reliability of estimations.
- Discern the defining characteristics of adept estimators, embodying unbiasedness, consistency, and relative efficiency.
- Specify the benchmarks for making choices among alternative estimators.