Given below are two statements:
Statement I: The standard deviation of a sampling distribution of a statistic is often called as 'standard error.
Statement II: When number of samples taken from a population is between 30 to 60. they are called as small samples.
In the light of the above statements, choose the most appropriate answer from the options given below:

Correct option is B

Both Statement I and Statement II are incorrect.
Statement I is incorrect because the standard deviation of a sampling distribution of a statistic, commonly referred to as the standard error, is used only under certain conditions. While this statement may be true in some contexts, the phrasing "often called" without context makes it inaccurate as a blanket rule. Standard error specifically applies to the variability of sample means around the population mean.
Statement II is incorrect because in statistics, small sample sizes are generally considered to be those with fewer than 30 observations, not between 30 to 60. A sample size of 30 or more is often deemed sufficient for applying the Central Limit Theorem, meaning that the distribution of the sample mean will approach normality.
Information Booster: 1. The standard error (SE) decreases as sample size increases, making larger samples more reliable for estimation.
2. Central Limit Theorem (CLT) is crucial when sample sizes are large (typically n ≥ 30), as it helps in approximating normality.
3. Small sample sizes (n < 30) often require specialized statistical techniques like the t-distribution for analysis.
4. Standard deviation measures the spread of data within a single sample, while standard error measures the spread of the sample means across multiple samples.
5. Larger samples reduce the impact of outliers and provide a more precise estimate of the population parameter.
6. Large samples (n ≥ 30) are generally preferred in empirical research because they offer higher statistical power and more robust conclusions.