Question

For each sample size, how does the mean of x compare with the population mean?

Do the standard deviations for each sample size match the population standard deviation? What happens to the standard deviation of x as n gets larger?

Answer 1

For each sample size, how does the mean of x compare with the population mean?

The mean of sample for any sample is equal to the population mean

Do the standard deviations for each sample size match the population standard deviation? What happens to the standard deviation of x as n gets larger?

No, the sample standard deviation do not match the population standard deviation.

The population standard deviation be and sample standard deviation be s, n be the sample size

Then,

If the n gets larger the sample standard deviation tends to infinity