s k The set of the values of the statistic so obtained, one for each sample, constitutes the sampling distribution of the statistic. Standard Error The standard deviation of the sampling distribution of a statistic is known as its Standard Error abbreviated as S.E. The Standard Errors (S.E.) of some of the well-known statistics, for large samples, are given below, where n is the sample size, s is the population variance. Sl.
No. Statistic Standard Error . Sample mean ( x – ) s . Observed sample proportion ( p ) PQ n .
Sample standard deviation ( s ) s n . Sample variance ( s ) s n . Sample quartiles .36263 s . Sample median .25331 s .
Sample correlation coefficient ( r ) − r . . Computing standard error in simple cases Example . A server channel monitored for an hour was found to have an estimated mean of transactions transmitted per minute.
The variance is known to be . Find the standard error. Given s which implies s = , n = hour = min, X = /min Standard Error = s Example . Find the sample size for the given standard deviation and the standard error with respect of sample mean is .
Given s = , S.E. X = We know that S.E = s Therefore, ⇒ Taking Squaring on both sides we get n = = ≅ The required sample size is . Example . A die is thrown times and a throw of or is observed times.
Find the standard error of the proportion for an unbiased die . Solution : If the occurrence of or on the die is called a success, then Sample size = ; Number of Success = Sample proportion = p = Population proportion ( P ) = Prob (getting or when a die is thrown) XII Std - Business