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Question: Select the incorrect statement(s).
I. A sampling distribution of sample means is a distribution obtained by using the means computed from random samples of a specific size taken from a population.
II. Sampling error is the difference between the sample measure and the corresponding population measure.
III. The standard deviation of the sample means will always be larger than the standard deviation of the population.
IV. The standard deviation of the sample means is called the standard error of the mean.


A ) II and III only
B ) III only
C ) I only
D ) I and IV only

Steps to derive

1 Statement I: A sampling distribution of sample means is a distribution obtained by using the means computed from random samples of a specific size taken from a population.

2 Statement II: Sampling error is the difference between the sample measure and the corresponding population measure due to the fact that the sample is not a perfect representation of the population.

3 Statement III: The standard deviation of the sample means will be smaller than the standard deviation of the population, and it will be equal to the population standard deviation divided by the square root of the sample size.

4 Statement IV: The standard deviation of the sample means is called the standard error of the mean.

5 So, only statement III is incorrect.



Hence the right answer is Option B

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