Final answer:
Constructing a 99% confidence interval involves using a point estimate from sample data, calculating the standard error, and then using the critical value to determine the margin of error. The confidence interval indicates that we can expect 99% of similarly constructed intervals to contain the true population proportion, with certain factors possibly affecting survey outcomes outside the margin of error.
Step-by-step explanation:
Constructing a Confidence Interval for a Population Proportion
When a newsgroup wants to construct a 99% confidence interval for a population proportion, like the proportion of Americans favoring a Green initiative, they use data collected from a sample. In this case, out of 526 randomly selected Americans, 419 favored the initiative. To construct the interval, the point estimate is the sample proportion (p') and the margin of error is found using the critical value (z*) for the confidence level multiplied by the standard error of the sample proportion.
For a 99% confidence interval, the z* value is typically around 2.576. Using the formula for the standard error: SE=p'(1-p')/n, where n is the sample size, we can calculate the standard error and then the error bound for the proportion (EBP). The confidence interval is then the range from (p'-EBP) to (p'+EBP).
The interpretation of a confidence interval, in this context, is that we would expect about 99% of these intervals to contain the true population proportion if we were to repeat the sampling process many times, while about 1% would not.
Factors that could affect the outcome of such surveys and are not covered by the margin of error might include survey design flaws, non-response bias, wording of questions, or timing of the survey.
The width of the confidence interval is inversely related to the confidence level; decreasing the confidence level from 99% to 90% would result in a narrower interval because the z* value would be smaller, implying less certainty about the true value lying within that interval.