In a notched tensile fatigue test on a titanium specimen, the expected number of cycles to first acoustic emission (used to indicate crack initiation) is = 28,000, and the standard deviation of the number of cycles is a = 5000. Let X,, X2,..., X25 be a random sample of size 25, where each X, is the number of cycles on a different randomly selected specimen. Then the expected value of the sample a vx number of cycles until first emission is E(X) = u= 28,000, and the expected total number of cycles for the 70000 x specimens is E(T,) = nu = 25(28,000) = 700,000. The standard deviations of X and T, are 5000 = 1000 Vn OT. Vno = V25(5000) - 25000 If the sample size increases ton = 100, E(X) is unchanged but ox = 500 , half of its previous value (the sample size must be quadrupled v to halve the standard deviation of X.)
In a notched tensile fatigue test on a titanium specimen, the expected number of cycles to first acoustic emission (used to indicate crack initiation) is = 28,000, and the standard deviation of the number of cycles is a = 5000. Let X,, X2,..., X25 be a random sample of size 25, where each X, is the number of cycles on a different randomly selected specimen. Then the expected value of the sample a vx number of cycles until first emission is E(X) = u= 28,000, and the expected total number of cycles for the 70000 x specimens is E(T,) = nu = 25(28,000) = 700,000. The standard deviations of X and T, are 5000 = 1000 Vn OT. Vno = V25(5000) - 25000 If the sample size increases ton = 100, E(X) is unchanged but ox = 500 , half of its previous value (the sample size must be quadrupled v to halve the standard deviation of X.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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