Hey!!

We have a 90%-confidence interval. I want to check if the following statements are correct.

1. If double the sample, the possibility that the value that we are looking for is out of the confidence interval is smaller.

2. The bigger the standard error, the smaller the confidence interval.

Since the confidence interval is $\left (\overline{x}- Z_{a/2}\cdot s_x, \overline{x}+ Z_{a/2}\cdot s_x\right )$, where $s_x$ is the standard error, I think that the second statement is wrong and it should be that the bigger the standard error, the bigger the confidence interval.

Is this correct?

What about the first statement?