Question

Same as above, the standard deviation of the sample means is equal to: a) 2.45 22. What is the effect of choosing a larger sample size for the sampling distribution? a) mean increases, standard deviation unchanged 23.

Answer 1

23)

Let we have samples $X_{1},X_{2},...,X_{n}$ from the distribution having mean $\mu$ and standard deviation $\sigma$ then according to sampling distribution of sample mean $\overline{x}$ is $\overline{x}\sim AN(\mu_{\overline{x}}=\mu,\sigma_{\overline{x}}=\sigma/\sqrt{n})$

So if we choose large sample size n i.e. if we increase the sample size n mean $\mu_{\overline{x}}$ is unchanged and SD is decrease i.e if $n\rightarrow \infty$ then $\sigma/\sqrt{n}\rightarrow 0$

hence mean unchanged, standard deviation decreases

Note Q22 requires additional data (sd . n)

sd(sample mean) = sd/sqrt(n)  

Please rate