A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 13% chose chocolate pie, and the margin of error was given as + or -4 percentage points. Given specific sample data, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?

For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level, wider will be the confidence interval.

This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.

The confidence interval for a population proportion is given by the formula:

[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]

So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.

Hence 95% confidence interval will be wider than 80% confidence interval.