Answer to Question #105688 in Statistics and Probability for suresh

Question

When large samples are considered,

A> Standard deviation is more
B> Standard deviation is less
C> Standard deviation is unaffected since the samples considered are random samples
D> None of the above

Answer 1

When large samples are considered, standard deviation is less.

The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus the mean of the distribution of the means never changes. The standard deviation of the sample means, however, is the population standard deviation from the original distribution divided by the square root of the sample size. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.

So, the correct answer is B.