Question

As the sample size increases, which of the following are true:

I) The sample mean tends to fall closer to the population mean

II) The sampling distribution of the sample mean xbar approximates the population distribution

III) The standard deviation decreases.

Is the answer for this both I and III? if not please explain (wasnt sure about II)

Answer 1

I) The sample mean tends to fall closer to the population mean

II) The sampling distribution of the sample mean x(bar) approximates the population distribution

III) The standard deviation decreases.

All are correct.

as sample size increases it is general view that it give more closer results to population mean . same can in be understand by using larger n in confidence interval we get smaller margin of error and thus curve become narrow, getting closer to population mean.

........................

if you have any doubt ask in comment give thumbs up if you like work