A random sample of 100 students were randomly selected from your school and their average grade was recorded,as a percentage,for the 2010/2011 school year.In order to compute a bootstrap confidence interval for the mean,200 subsequent bootstrap samples were taken and the 200 resulting sample means were ordered from lowest to highest.The first 10 and last 10 ordered means are given below:
Use the percentile method to compute a 90% bootstrap confidence interval for the true average grade of all students at your school.
A)(60.44,80.98)
B)(61.22,80.57)
C)(63.01,78.13)
D)(61.22,79.33)
E)(61.67,80.57)

Question

A random sample of 100 students were randomly selected from your school and their average grade was recorded,as a percentage,for the 2010/2011 school year.In order to compute a bootstrap confidence interval for the mean,200 subsequent bootstrap samples were taken and the 200 resulting sample means were ordered from lowest to highest.The first 10 and last 10 ordered means are given below: 
Use the percentile method to compute a 90% bootstrap confidence interval for the true average grade of all students at your school.
A)(60.44,80.98) 
B)(61.22,80.57) 
C)(63.01,78.13) 
D)(61.22,79.33) 
E)(61.67,80.57)

Quizplus · Accepted Answer

We need to find the 5th and 95th percentile of the ordered bootstrap sample means.

The 5th percentile is the 10th value in the ordered list, which is 63.01.

The 95th percentile is the 190th value in the ordered list, which is 78.13.

Therefore, the 90% bootstrap confidence interval for the true average grade of all students at your school is (63.01, 78.13). The correct answer is C.

A Random Sample of 100 Students Were Randomly Selected from Your