Question

select the most appropriate response.
what would happen (other things being equal) to a confidence interval if you calculated a 95% confidence interval rather than a 99%
confidence interval?
○ it will be wider.
○ it will be narrower.
○ it will not change.
9 multiple choice 1 point
select the most appropriate response.
as sample size increases (other things being equal), what tends to happen to 95% confidence intervals?
○ they become wider.

Explanation:

First Question (Confidence Interval Change from 99% to 95%)

A confidence interval's width is related to the confidence level. A higher confidence level (like 99%) requires a wider interval to capture more possible values. So, reducing the confidence level from 99% to 95% makes the interval narrower as we need less coverage.

The standard error (part of the confidence interval formula) is inversely related to the square root of the sample size ($SE=\frac{\sigma}{\sqrt{n}}$ for population standard deviation $\sigma$ and sample size $n$). As sample size $n$ increases, standard error decreases. A smaller standard error leads to a narrower confidence interval (since confidence interval = sample statistic ± margin of error, and margin of error is related to standard error). So, as sample size increases, 95% confidence intervals become narrower (the option "They become wider" is incorrect; the correct answer, though not fully shown, would be they become narrower). But based on the given option to analyze, the "They become wider" is wrong. However, to answer the question's intent, when sample size increases, 95% confidence intervals narrow.

Answer:

It will be narrower.

Second Question (Sample Size Increase and 95% Confidence Interval)