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# A sample of seven concrete blocks had their crushing ISBN: 9780073401331 38

## Solution for problem 26SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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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. Step-by-Step Solution:

Step 1 of 4</p>

a) Here we have to find the 95% confidence interval for mean of bootstrap by using method-1

Let represents the 100 percentile

Let represents the 100(1- percentile

The 95% confidence intervals are , )=( , )

=( = = (1305.5, 1462.1)

The 95% confidence interval using method 1 is (1305.5, 1462.1)

Step 2 of 4</p>

b) Here we have to find the 95% confidence interval for mean of bootstrap by using method 2

Now find mean of given 7 values =1385.1

The 95% confidence intervals are ( )

=( )

From above write the and values

=[2(1385.1)-1462.1, 2(1385.1)-1305.5)

=(1308.1, 1464.7)

Hence the 95% confidence intervals by using method 2 is (1308.1,1464.7)

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The full step-by-step solution to problem: 26SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: bootstrap, Strength, mean, compressive, Using. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “A sample of seven concrete blocks had their crushing strength measured in MPa. The results were1367.6 1411.5 1318.7 1193.6 1406.21425.71572.4 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.” is broken down into a number of easy to follow steps, and 184 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 26SE from 5 chapter was answered, more than 261 students have viewed the full step-by-step answer.

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