Question

QUESTION 1 Suppose we have a sample size of 100 and calculate a confidence interval. What will happen to that interval if we then get a sample size of 200 (all else equal). It will become narrower It will become wider. It will remain the same, because the mean is not changing It will get closer to 1.96.

Answer 1

For population mean the
(1-0) 100%
confidence interval is
1-a2,n-1

For population proportionthe
(1-0) 100%
confidence interval is $\widehat{p}\pm z_{1-\alpha /2}\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}$

In both cases, we can see that the width of the CI

1 width x n

So when the sample size increases, the width of the confidence interval becomes narrower.

First choice is correct.