Question

WHICH OF THE FOLLOWING SAMPLES WILL HAVE THE SMALLEST VALUE FOR THE ESTIMATED STANDARD ERROR? a. n=25 with s^2 = 100 b. n=25 with s^2 = 400 c. n=100 with s^2 = 100 d. n=100 with s^2 = 400

Answer 1

Sampling distribution of the sample mean, I follows normal distribution with the mean, u and variance, —, where u is the population mean and is the population variance if the sample size is large enough irrespective of the population distribution. The standard deviation of sample mean is known as standard error. Therefore, I Variance Standard error (SE)=, Sample size The calculation of standard error for different values of sample size and variance is shown in the below table. Sample size (n) Variance (52) Standard error (SE) = 100 SE = | 25 400 100 100 100 400 Therefore, the smallest standard error is obtained as 1 when the sample size is 100 and variance is 100. Hence, the correct answer choice is option (c).