For simple random sampling with replacement Ave (sample variance) = Population v

Question

For simple random sampling with replacement Ave (sample variance) = Population variance. Which of following are always true? Ave(sample standard deviation) = Population standard deviation Ave(sample standard deviation) is greater than or equal to population standard deviation Variance(sample standard deviation) = Population variance/n Variance(sample standard deviation) is less than or equal to population variance Ave(sample standard deviation) is less than or equal to population standard deviation

Explanation / Answer

If Average(Sample variance) = Population variance, then

A. Ave(Sample standard deviation) = Population standard deviation always stands true.

Sample standard deviation is an unbiased estimate of population standard deviation. Hence, A is true and B and E are false.

Also, nothing can be said about the variance of sample standard deviation.

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