Answer to Question #105691 in Statistics and Probability for suresh

Question

When we consider multiple random samples from a given population, the mean of these samples tend to be closer to the population mean

A> If sample size of these multiple samples are increased
B> If sample size of these multiple samples are decreased
C> Increasing or decreasing the sample size of these multiple samples makes no difference as the samples considered are true random samples
D> None of the above

Answer 1

The correct answer is A) If sample size of these multiple samples are increased the mean of these samples tend to be closer to the population mean.

$E=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ is the margin of error.

We see that if sample size increases margin of error decreases.

From here it follows that $n=(\frac{z_{\alpha/2}\sigma}{E})^2.$