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 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

Quizplus · Accepted Answer

To compute a 90% bootstrap confidence interval using the percentile method, we need to find the 5th and 95th percentiles of the ordered sample means.

From the given list of ordered means, the 5th percentile is the 10th observation (since 5% of 200 is 10). The 10th observation is 63.01.

Similarly, the 95th percentile is the 190th observation (since 95% of 200 is 190). The 190th observation is 78.13.

Therefore, the 90% bootstrap confidence interval is (63.01, 78.13).

The closest choice to this interval is C, (63.01, 78.13).

A Random Sample of 100 Students Were Randomly Selected from Your