Final answer:
The large sample confidence interval formula is typically used when the sample size is greater than 30, but conditions such as np and nq should be greater than 5. Larger confidence levels yield wider intervals, while larger sample sizes provide narrower intervals and more precision.
Step-by-step explanation:
The large sample confidence interval formula for estimating the population proportion is generally safe to use when the sample size n is greater than 30. However, it is important to ensure that the sample meets the condition where both np and nq are greater than 5 for the normal approximation to be valid. In situations where the sample size is smaller or the distribution of the sample is highly skewed, alternative methods such as the “plus-four confidence interval for p” method are recommended, especially when the confidence level is 90% or greater and the sample size is at least 10.
When constructing confidence intervals, an increase in the confidence level will result in a wider interval, indicating that there's a higher probability that the interval contains the true population proportion. Conversely, a decrease in the confidence level will create a narrower interval. It's crucial to remember that a larger sample size can reduce the error bound and consequently create a more precise confidence interval, which is particularly useful when determining the population proportion with a high degree of certainty.