Question

Suppose you calculate a 95% and 90% confidence interval for the true proportion of college students with student loan. Which of the following must be true.

a) The 95% confidence interval is the same length as the 90% confidence interval
b) There is no way to tell form the given information
c) The 95% confidence interval is narrower than the 90% confidence interval.
d) The 95% confidence interval is wider than the 90% confidence interval.

Answer 1

The 95% confidence interval is narrower than the 90% confidence interval.

Step-by-step explanation:

The 95% confidence interval is narrower than the 90% confidence interval. This is because as the confidence level increases, the margin of error also increases, resulting in a wider interval. Conversely, as the confidence level decreases, the margin of error decreases, resulting in a narrower interval.

When you increase the confidence level (from 90% to 95% in this case), the corresponding interval becomes wider because you are increasing the level of certainty, which means you need to include a larger range of values. Therefore, a 95% confidence interval is generally wider than a 90% confidence interval for the same data.

So, the correct relationship between the 95% and 90% confidence intervals is that the 95% interval is wider.