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 .
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa77d52c3-5480-47b7-8f2c-45b52855bf59%2Fb113b09a-a573-43e1-8c16-83362cdf3f81%2Fk0r6xbm_processed.png&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa77d52c3-5480-47b7-8f2c-45b52855bf59%2Fb113b09a-a573-43e1-8c16-83362cdf3f81%2Fe6r2fcr_processed.png&w=3840&q=75)
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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