Let X1, X₂, ..., X, be a random sample from a normal distribution with unknown mean and known variance 2. Which statement is correct? x-μ (1) is a pivotal quantity for μ and a 100(1-a) % confidence interval for based on that is ± z o/√n X-μ (11) is a pivotal quantity for μ and a 100(1 − a)% confidence interval for μ based on that is o/√n X ± %a/?
Let X1, X₂, ..., X, be a random sample from a normal distribution with unknown mean and known variance 2. Which statement is correct? x-μ (1) is a pivotal quantity for μ and a 100(1-a) % confidence interval for based on that is ± z o/√n X-μ (11) is a pivotal quantity for μ and a 100(1 − a)% confidence interval for μ based on that is o/√n X ± %a/?
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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![Let X1, X₂, ..., Xn be a random sample from a normal distribution with unknown mean μ and known
variance 2. Which statement is correct?
x-μ
(1) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for μ based on that is X ± %
o/√√√n
X-μ
(11) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for based on that is
o/√√n
X ± %α/2]
X-μ
(III) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for μ based on that is
S√√n
Ñ ±tn-1,0/2 √²
X-H
S/√√n
X±tn-1,a
(IV) is a pivotal quantity for μ and a 100(1 — a)% confidence interval for μ based on that is
S
√n
O (1)
O (III)
O (IV)
O (II)
o
√n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f06f1bb-c942-497f-ad85-135a50a5e6e3%2F32b1b120-e5f9-4238-b1df-aaa98da0f863%2Fx4qs5en_processed.png&w=3840&q=75)
Transcribed Image Text:Let X1, X₂, ..., Xn be a random sample from a normal distribution with unknown mean μ and known
variance 2. Which statement is correct?
x-μ
(1) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for μ based on that is X ± %
o/√√√n
X-μ
(11) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for based on that is
o/√√n
X ± %α/2]
X-μ
(III) is a pivotal quantity for μ and a 100(1 — a) % confidence interval for μ based on that is
S√√n
Ñ ±tn-1,0/2 √²
X-H
S/√√n
X±tn-1,a
(IV) is a pivotal quantity for μ and a 100(1 — a)% confidence interval for μ based on that is
S
√n
O (1)
O (III)
O (IV)
O (II)
o
√n
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