Question

My 95% confidence interval of the proportion of times someone goes "Awww" when they see Artemis is (.67, .89). I calculated this using 1,000 bootstrap samples, where my original sample was 100 showings. For the following scenarios, please pick which of the following confidence intervals would be most appropriate. Explain Why.

a. (.72, .83)

b. (.67, .89)

c. (.52, .99)

1. Instead finding a 90% confidence interval.

Answer 1

Solution:

The 95% confidence interval found is (0.67,0.89). Now we have to determine the most appropriate 90% confidence interval.

The correct option is:

a. (.72, .83)

Explanation:

We know that as the confidence level of the confidence interval decreases the width of the confidence interval decreases as well. Since in the given question, the confidence level is reduced from 95% to 90%, therefore, we have to choose the option with the width less than the width of the 95% confidence interval.

The width of the 95% confidence interval is 0.89-0.67=0.22

Among the given options, the confidence interval with a width of less than 0.22 is:

(0.72,0.83) with width 0.83-0.72=0.11.

Therefore, the correct option is a. (.72,.83)