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
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Author:Amos Gilat
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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
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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