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RANK CORRELATION

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Problem 1. The lifetime of a device of type A is Exponentially distributed with mean 10 (years) while the lifetime of a device of type B has a Gamma distribution with parameters (cid:11) = 2 and (cid:21) = 1=10. It is known that 40% of the devices in the factory are of type A and the remaining 60% are of type B. Let X be the lifetime of a randomly chosen device. (a) Compute the mean and the variance of X. Solution 2.Exponentially distributed MTBF = 500 h t = 600 h MTBF = 1/? ? = 1/MTBF = 2*10^-3 fr/hr R(t) = e^-?t R(600) = e^-2*10^-3*600 R(600) =0.30119 = 30.119% --> Probability of successfull/survive R(T+t) = R(t) R(T+100) = R(100) R(100) = e^-2*10^-3*100 R(100) = 0.81873 = 81.873 Probability of failure, U(100) = 1 - R(100) U(100) = 0.18127 = 18.873 %.

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- Problem 3 - A college algebra teacher want to know whether there is a negative relationship between number of times a student is absent from class and performance in class. At the end of the semester, he ranks each of his 35 students on two variables, assigning a rank of 1 to the student with the most absences and a rank of 1 to the student with the highest class rank (See accompanying data). Do a one tailed Spearman Rank Correlation test at alpha=0.01 of the null and alternative hypotheses: Ho: Class performance has no rank correlation with number of absences. Ha: Class performance has a negative rank correlation with number of absences. Absences Performance 10.5 25 17.5 11 28 17 24 18 9 33 33.5 35 2 1 19 5 17.5 22 1 34 35 3 7.5 27 25 12 10.5 4 33.5 10 3 26 22 19 27 13 7.5 6 29 29 15.5 28 20 16 4.5 32
- 12 24 31 2 13 23 32 9 6 30 30 21 21 15 14 7 4.5 31 26 20 15.5 8 23 14 a) Find the value of the test statistic b) Find the critical value (from the appropriate table) c) State the statistical decision d) State the decision in term of the problem Solution (a) The test statistic is -0.311 (b) the critical value is -0.430 (c) Since -0.311 is larger than -0.43, we do not reject Ho. (d) So we can not conclude that Class performance has a negative rank correlation with number of absences.

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