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Chapter 8: Q1E (page 325)

For each of the following assertions, state whether it is a legitimate statistical hypothesis and why:

\(\begin{array}{l}{\rm{a}}{\rm{. H: \sigma > 100}}\\{\rm{c}}{\rm{. H: s }} \le {\rm{.20}}\\{\rm{e}}{\rm{. H:}}\overline {{\rm{ X}}} {\rm{ - }}\overline {\rm{Y}} {\rm{ = 5}}\end{array}\) \(\begin{array}{l}{\rm{b}}{\rm{. H: }}\widetilde {\rm{x}}{\rm{ = 45}}\\{\rm{d}}{\rm{. H: }}{{\rm{\sigma }}_{\rm{1}}}{\rm{/}}{{\rm{\sigma }}_{\rm{2}}}{\rm{ < 1}}\end{array}\)

\({\rm{f}}{\rm{. H: \lambda }} \le {\rm{.01}}\), where \({\rm{\lambda }}\) is the parameter of an exponential distribution used to model component lifetime

Short Answer

Expert verified

a)Yes , b) No, c) No, d) Yes, e) No, f) Yes.

Step by step solution

01

Step 1:Statistical hypothesis.

A statistical hypothesis, or just hypothesis, is a claim or assertion either about the value of a single parameter (population characteristic or characteristic of a probability distribution), about the values of several parameters, or about the form of an entire

probability distribution.

02

Step 2:Solution for part a), b) and c).

a)Yes, it is legitimate. It is a claim about the value of a parameter.

b)No, it is not legitimate. It is not a claim about the value of a parameter(the sample median is not a parameter).

c)No, it is not legitimate. It is not a claim about the value of a parameter(the same standard deviation is not a parameter).

03

Step 3:Solution for part d), e) and f).

d)Yes, it is legitimate. It is a claim that the standard deviation of the one population exceeds other.

e)No, it is not legitimate. It is not a claim about the value of a parameter(the \(\overline X \)and\(\overline Y \) are statistics not a parameter).

f)Yes, it is legitimate. It is a claim about the value of a parameter.

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