Given below are two statements:

Statement I: The standard deviation of a sampling distribution of a statistic is often called a 'standard error'.

Statement II: When the number of samples taken from a population is between 30 to 60, they are called small samples.

In light of the above statements, choose the most appropriate answer from the options given below:

Statement I: The standard deviation of a sampling distribution of a statistic is often called a 'standard error'.

Key Points

• Measures of variability include standard deviation and standard error.
• Standard error estimates the variability across samples of a population while standard deviation reflects variability within a sample
• The standard error of the sample means depends on both the standard deviation and the sample size, by the simple relation

SE = SD/√(sample size)

SE - Standard Error

SD - Standard Deviation

Hence, the statement is incorrect.

Statement II: When the number of samples taken from a population is between 30 to 60, they are called small samples.

Key PointsLarge sample theory:

• If the sample size n is greater than 30 (n≥30) it is known as a large sample.
• For large samples, the sampling distributions of statistics are normal(Z test).
• A study of the sampling distribution of statistics for a large sample is known as the large sample theory.

• If the sample size n is less than 30 (n<30), it is known as a small sample.
• For small samples, the sampling distributions are t, F, and χ2 distribution.
• A study of sampling distributions for small samples is known as the small sample theory.

Hence, the number of samples taken from a population between 30 to 60 is called a large sample.

Hence, statement II is also incorrect. 

So, Both Statement I and Statement II are incorrect.