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# Refer to Exercise 22.a. Generate 10,000 bootstrap samples ISBN: 9780073401331 38

## Solution for problem 27SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Problem 27SE

Refer to Exercise 22.

a. Generate 10,000 bootstrap samples from the data in Exercise 22. Find the bootstrap sample mean percentiles that are used to compute a 99% confidence interval.

b. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 1 as described on page 386.

C. Compute a 99% bootstrap confidence interval for the mean compressive strength, using method 2 as described on page 386.5.

REFERENCE EXERCISE: 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 3</p>

a) We have to find the 99% confidence interval

From the given data mean And the standard deviation =114.93

After generating the bootstrap sample    The 99% confidence interval is

( , )=( = = (1270.15, 1495.155)

Hence the 99% confidence interval is (1270.15, 1495.155)

Step 2 of 3</p>

b)  Here we have to find the 99% confidence interval for mean of bootstrap by using method- 1

The 99% confidence intervals are , )=( , )

=( = = (1283.4, 1483.8)

The 99% confidence interval using method 1 is (1283.4, 1483.8)

Step 3 of 3

##### ISBN: 9780073401331

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