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: First 10: 59.41,59.56,60.13,60.44,61.22,61.67,62.45,62.48,62.56,63.01
Last 10: 78.13,78.25,78.67,79.12,79.33,80.57,80.98,81.88,81.99,82.71
Use the percentile method to compute a 95% bootstrap confidence interval for the true average grade of all students at your school.
A)(60.44,80.98)
B)(61.67,80.57)
C)(61.22,79.33)
D)(61.22,80.57)
E)(63.01,78.13)

Question

Quizplus · Accepted Answer

The percentile method involves finding the 2.5th and 97.5th percentiles of the ordered bootstrap sample means to form the confidence interval. In this case, the 2.5th percentile is the 5th smallest value (since there are 200 samples) and the 97.5th percentile is the 195th smallest value. Looking at the ordered list, we see that the 5th smallest value is 61.22 and the 195th smallest value is 80.57. Thus, our 95% bootstrap confidence interval for the true average grade is (61.22, 80.57). Choice D is the only option that contains both values.

A Random Sample of 100 Students Were Randomly Selected from Your