Why are these statements false?

[emilybatman]

Hello,

I was doing a practice test and I got two questions wrong. The answer key said that these two statements were false:

As sample size increases, the standard deviation of the sampling distribution and the standard deviation of the population are increasingly similar.
-and-
For the standard normal curve, the area to the left of p=0.1 is the same as the area to the right of p=0.9

Can anyone tell me why these two statements are false?

Thank you!!

 

[blubblub]

For the first one. Think about the formula for the standard deviation of the sampling distribution (standard error), this is standard deviation of population divided by square root of sample size. Now what will happen with the standard deviation of the population if the sample size increases? And which one will change in the formula for standard error?

As for the second one I'm not sure. The only thing I can come up with is that the areas are not right or left from a p-value, but from z-values. So the area to the left at z = 0.1 is not the same as the area to the right at z = 0.9, but I might be missing something here.