(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 larger than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 95% 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 larger than the standard deviation of the population under study.
(iii) For a sampling distribution of the means, 95% 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

(i) is correct because the standard error of the mean is indeed defined as the standard deviation of the sampling distribution of the sample means. (iii) is correct in the sense that for a normally distributed sampling distribution of the mean, approximately 95% of the sample means would fall within ±1.96 standard deviations of the mean. (ii) is incorrect because the standard deviation of the sampling distribution of the mean (standard error) is typically smaller than the standard deviation of the population, not larger.

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

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