In the calculation for confidence intervals, larger samples give narrower intervals. We are able to estimate a population proportion more precisely with larger sample size. Therefore, the width decreases as the sample size increases.
As the confidence level increases the width of the confidence interval also increases. A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means that the interval is larger.
In summary, the width of a confidence interval decreases as the sample size increases and increases as the confidence level increases.
Therefore, the correct option will be "The interval widens if the sample size decreases and confidence level stays the same."
