(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means.
(ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 90% of the means would be between $\pm$ 1.96 standard deviations.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means. 
(ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 90% of the means would be between $\pm$ 1.96 standard deviations.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Quizplus · Accepted Answer

Statement (i) is correct as this is the definition of the standard error of the mean. Statement (ii) is generally true but not always, as the standard deviation of the population may be unknown or impossible to calculate, in which case the standard deviation of the sampling distribution is estimated using the sample. Statement (iii) is incorrect, as 90% of the means would be between 1.64 standard deviations, not 1.96, if we assume a normal distribution. However, if the sample size is small or the population distribution is non-normal, this may not hold true.

(I the Standard Error of the Mean Is the Standard ±\pm±

(I the Standard Error of the Mean Is the Standard $\pm$