Q.26 Standard error is
(A) the probability of a type I error in a statistical test
(B) the error in estimating a sample standard deviation
(C) the standard deviation of a variable that follows standard normal distribution
(D) the standard deviation of distribution of sample means

Standard error is the standard deviation of the distribution of sample means, measuring how much sample means vary from the true population mean across repeated samples. The correct answer to this multiple-choice question is (D). This concept is fundamental in statistics for understanding sampling variability.

Option Analysis

• (A) the probability of a type I error in a statistical test: Incorrect, as type I error (alpha) is the false positive rate in hypothesis testing, unrelated to variability of sample statistics.​

• (B) the error in estimating a sample standard deviation: Incorrect, since standard error concerns sample means or other statistics, not errors in standard deviation estimation itself.​

• (C) the standard deviation of a variable that follows standard normal distribution: Incorrect, as the standard normal distribution has a fixed standard deviation of 1, not variable like standard error.​

• (D) the standard deviation of distribution of sample means: Correct, as standard error (SE) quantifies the spread of the sampling distribution of the mean, calculated as SE=s/√n  where $s$ is sample standard deviation and $n$ is sample size.​

Introduction: Understanding Standard Error in Statistics
Standard error in statistics measures the precision of a sample mean as an estimate of the population mean. Often confused with standard deviation, standard error specifically refers to the standard deviation of the distribution of sample means from repeated sampling. This key metric helps assess how closely your sample reflects the population, shrinking as sample size grows.​

What is Standard Error?

Standard error quantifies variability in sample statistics, especially the mean. If you take many samples from a population and calculate each mean, those means form a sampling distribution whose standard deviation is the standard error. Formula: SE=σ/√n  (population) or SE=s/√n  (sample), where larger $n$ reduces SE.​

Standard Error vs. Standard Deviation

Standard deviation describes data dispersion around the sample mean, while standard error evaluates estimate reliability.​

Applications in Research

• Builds confidence intervals: xˉ±z⋅SExˉ±z⋅SE.

• Hypothesis testing: Smaller SE means tighter intervals.

• Central Limit Theorem: Sampling distribution approximates normal for large $n$.​
  In biotechnology research, standard error refines enzyme kinetics or gene expression means from replicates.​