Problem 26SE
A sample of seven concrete blocks had their crushing strength measured in MPa. The results were
1367.6 
1411.5 
1318.7 
1193.6 
1406.2 
1425.7 
1572.4 



Ten thousand bootstrap samples were generated from these data, and the bootstrap sample means were arranged in order. Refer to the smallest mean as Y1 the second smallest as Y2, and so on, with the largest being Y10,000. Assume that Y50 = 1283.4, Y51 = 1283.4, Y100 = 1291.5, Y101 = 1291.5, Y250 = 1305.5, Y251 = 1305.5, Y500 = 1318.5, Y501 = 1318.5, Y9500= 1449.7, Y950l = 1449.7, Y9750 = 1462.1, Y9751 = 1462.1, Y9900 = 1476.2, Y9901 = 1476.2, Y9950 = 1483.8, and Y9951 = 1483.8.
a. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 1 as described on page 386.
b. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 2 as described on page 386.
c. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 1 as described on page 386.
d. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 2 as described on page 386.
Solution
Step 1 of 4
a) Here we have to find the 95% confidence interval for mean of bootstrap by using method1
Let represents the 100 percentile
Let represents the 100(1percentile
The 95% confidence intervals are
, )=(, )
=(
=
= (1305.5, 1462.1)
The 95% confidence interval using method 1 is (1305.5, 1462.1)