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d. Among untreated patients, the probability of remaining fracture free for at least 7 months is 0 < null < 1. We want to conduct a .05-level test of Ho: 7 = null VS. Ha : null. Using results from (c), find a test statistic, its distribution under the null, and the rejection region of the test. hint: you can plug in for 0 in the test statistic and maintain the asymptotic distribution from (c). Invert the test from (d) to construct a 95% confidence interval estimator for .

d. Among untreated patients, the probability of remaining fracture free for at least 7 months is 0 < null < 1. We want to conduct a .05-level test of Ho: 7 = null VS. Ha : null. Using results from (c), find a test statistic, its distribution under the null, and the rejection region of the test. hint: you can plug in for 0 in the test statistic and maintain the asymptotic distribution from (c). Invert the test from (d) to construct a 95% confidence interval estimator for .

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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For the two attchaed images, kindly answer part d and e, clearly showing all steps. Thank you

d. Among untreated patients, the probability of remaining fracture free for at least T months is 0 < Vnull < 1. We want to conduct a .05-level test of Ho : , = Vnull VS. Ha : 4, # Vnull- Using results from (c), find a test statistic, its distribution under the null, and the rejection region of the test. hint: you can plug in ô for 0 in the test statistic and maintain the asymptotic distribution from (c). Invert the test from (d) to construct a 95% confidence interval estimator for 7. е.
Transcribed Image Text:d. Among untreated patients, the probability of remaining fracture free for at least T months is 0 < Vnull < 1. We want to conduct a .05-level test of Ho : , = Vnull VS. Ha : 4, # Vnull- Using results from (c), find a test statistic, its distribution under the null, and the rejection region of the test. hint: you can plug in ô for 0 in the test statistic and maintain the asymptotic distribution from (c). Invert the test from (d) to construct a 95% confidence interval estimator for 7. е.
Patients diagnosed with osteoporosis are at risk of bone fractures. To reduce the risk, a new oral bisphosphonate (BP) drug has been developed but its efficacy is unknown. Researchers randomly select n patients to treat with the new drug. After treatment start, patients are followed up until their first fracture. Let X; > 0 be the time-to-first fracture after treatment initiation (measured in months) for the ith subject, where i = 1,2,...,n. We iid model the fracture times as X1, X2, .., Xn Exp(0). Here, X - Exp(0) denotes the exponential distribution with scale 0 > 0 having density f(x) = je-jz for x > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. For some fixed constant T > 0, let w, = P(X > 7). Ideally, the probability will be high - indicating that osteoporosis patients on the new BP drug will remain fracture free for at least 7 months with high probability. a. Integrate the given density to find an expression for v, in terms of 0 and t. b. Find the MLE of 0, denoted ô. Verify it is a max. Find the asymptotic distribution of n(ô – 0) 2?. Compute the MLE of w7, V7. Find the asymptotic distribution of n(,-ab7) 2 ?. с.
Transcribed Image Text:Patients diagnosed with osteoporosis are at risk of bone fractures. To reduce the risk, a new oral bisphosphonate (BP) drug has been developed but its efficacy is unknown. Researchers randomly select n patients to treat with the new drug. After treatment start, patients are followed up until their first fracture. Let X; > 0 be the time-to-first fracture after treatment initiation (measured in months) for the ith subject, where i = 1,2,...,n. We iid model the fracture times as X1, X2, .., Xn Exp(0). Here, X - Exp(0) denotes the exponential distribution with scale 0 > 0 having density f(x) = je-jz for x > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. For some fixed constant T > 0, let w, = P(X > 7). Ideally, the probability will be high - indicating that osteoporosis patients on the new BP drug will remain fracture free for at least 7 months with high probability. a. Integrate the given density to find an expression for v, in terms of 0 and t. b. Find the MLE of 0, denoted ô. Verify it is a max. Find the asymptotic distribution of n(ô – 0) 2?. Compute the MLE of w7, V7. Find the asymptotic distribution of n(,-ab7) 2 ?. с.
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