If 8 short range rockets of one kind have a mean target error of x₁ = 98 metres with a standard deviation of s₁ = 18 metres while 10 rockets of another kind have a mean target error of x₂ = 76, with standard deviation of s₂ = 15 metres. Assume that the target errors for the two types of rockets are normally distributed and that they have a common variance. (a) Given that the common variance is not known, state why the statistic T given (x₁ - x₂) - (μ₁ −μ₂) by T is pivotal quantity stating clearly its distribution
If 8 short range rockets of one kind have a mean target error of x₁ = 98 metres with a standard deviation of s₁ = 18 metres while 10 rockets of another kind have a mean target error of x₂ = 76, with standard deviation of s₂ = 15 metres. Assume that the target errors for the two types of rockets are normally distributed and that they have a common variance. (a) Given that the common variance is not known, state why the statistic T given (x₁ - x₂) - (μ₁ −μ₂) by T is pivotal quantity stating clearly its distribution
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![If 8 short range rockets of one kind have a mean target error of x₁ = 98 metres with a
standard deviation of s₁ = 18 metres while 10 rockets of another kind have a mean
target error of x₂ = 76, with standard deviation of s₂ = 15 metres. Assume that the
target errors for the two types of rockets are normally distributed and that they have
a common variance.
(a) Given that the common variance is not known, state why the statistic T given
(x₁ - x₂) - (μ₁ −μ₂)
is a pivotal quantity, stating clearly its distribution.
-
by T =
1 1
SP₁ - +
(b)
(c)
Where S=
n₁ n₂
(n₁ − 1)s² + (n₂ − 1)²
n₁ + n₂-2
Find the point estimate of μ₁ - 1₂.
Use the pivot quantity in (a) to derive a two sided (1-a)100% confidence
interval for the difference between two population means, μ₁ - ₂.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eea6dc0-72ac-4bb4-af82-e9b744ff9a04%2F825fabcf-f024-42f2-8891-89d252333993%2Fqt2ubqu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If 8 short range rockets of one kind have a mean target error of x₁ = 98 metres with a
standard deviation of s₁ = 18 metres while 10 rockets of another kind have a mean
target error of x₂ = 76, with standard deviation of s₂ = 15 metres. Assume that the
target errors for the two types of rockets are normally distributed and that they have
a common variance.
(a) Given that the common variance is not known, state why the statistic T given
(x₁ - x₂) - (μ₁ −μ₂)
is a pivotal quantity, stating clearly its distribution.
-
by T =
1 1
SP₁ - +
(b)
(c)
Where S=
n₁ n₂
(n₁ − 1)s² + (n₂ − 1)²
n₁ + n₂-2
Find the point estimate of μ₁ - 1₂.
Use the pivot quantity in (a) to derive a two sided (1-a)100% confidence
interval for the difference between two population means, μ₁ - ₂.
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