In Example 5.20 the following measurements were given for the cylindrical compressive strength (in MPa) for 11 beams:

One thousand bootstrap samples were generated from these data, and the bootstrap sample means were arranged in order. Refer to the smallest value as Y₁, the second smallest as Y₂, and so on, with the largest being Y₁₀₀₀. Assume that Y₂₅ = 38.3818, Y₂₆ = 38.3818, Y₅₀ = 38.3909, Y₅₁ = 38.3918, Y₉₅₀ = 38.5218, Y₉₅₁ = 38.5236, Y₉₇₅ = 38.5382, and Y₉₇₆ = 38.5391.

a. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 1.

b. Compute a 95% bootstrap confidence interval for the mean compressive strength, using method 2.

c. Compute a 90% bootstrap confidence interval for the mean compressive strength, using method 1.

d. Compute a 90% bootstrap confidence interval for the mean compressive strength, using method 2.

Method 1:

Method 2:

38.43 38.43 38.39 38.83 38.45 38.35 38.43 38.31 38.32 38.48 38.50