A sample of seven concrete blocks had their crushing strength measured in MPa. The

Chapter 5, Problem 26

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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 \(Y_{1}\), the second smallest as \(Y_{2}\), and so on, with the largest being \(Y_{10,000}\). Assume that \(Y_{50}=1283.4, Y_{51}=1283.4, Y_{100}=1291.5, Y_{101}=1291.5, Y_{250}=1305.5, Y_{251}=1305.5\), \(Y_{500}=1318.5, Y_{501}=1315.5, Y_{9500}=1449.7, Y_{9501}=1449.7, Y_{9750}=1462.1, Y_{9751}=1462.1, Y_{9900}=1476.2\), \(Y_{9901}=1476.2, Y_{9950}=1483.8, \text { and } Y_{9951}=1483.8\)

a. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 1 as described on page 390.

b. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 2 as described on page 390.

c. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 1 as described on page 390.

d. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 2 as described on page 390.

Equation Transcription:

       

     

     

Text Transcription:

Y1      

Y2      

Y10,000    

Y50=1283.4, Y51=1283.4, Y100=1291.5, Y101=1291.5, Y250=1305.5, Y251=1305.5

Y500=1318.5, Y501=1315.5, Y9500=1449.7, Y9501=1449.7, Y9750=1462.1, Y9751=1462.1, Y9900=1476.2

Y9901=1476.2, Y9950=1483.8, and Y9951=1483.8