Answer :
To address the problem, we start by identifying the claim and its complement, then determine which hypothesis corresponds to the null hypothesis ([tex]$H_0$[/tex]) and which corresponds to the alternative hypothesis ([tex]$H_a$[/tex]).
Given the claim:
[tex]\[\sigma = 13\][/tex]
First, we need to find the complement of the claim. The complement of the statement "[tex]\(\sigma = 13\)[/tex]" is "[tex]\(\sigma \neq 13\)[/tex]".
So, the complement is:
[tex]\[\sigma \neq 13\][/tex]
In hypothesis testing, the null hypothesis ([tex]$H_0$[/tex]) typically represents the default or initial claim, and the alternative hypothesis ([tex]$H_a$[/tex]) represents the complement or the opposing outcome.
Thus:
[tex]\[ H_0: \sigma = 13 \][/tex]
[tex]\[ H_a: \sigma \neq 13 \][/tex]
Now we look at the given choices to identify which one correctly states [tex]$H_0$[/tex] and [tex]$H_a$[/tex]:
A. [tex]\(H_0: \sigma=13\)[/tex]
B. [tex]\(H_0: \sigma=13\)[/tex]
C. [tex]\(H_0: \sigma \leq 13 \quad H_a: \sigma < 13 \quad H_a: \sigma \leq 13 \quad H_a: \sigma=13\)[/tex]
D. [tex]\(H_0: \sigma \neq 13\)[/tex]
E. [tex]\(H_0: \sigma=13\)[/tex]
F. [tex]\(H_0: \sigma < 13 \quad H_a: \sigma=13 \quad H_a: \sigma > 13 \quad H_a: \sigma=13\)[/tex]
G. [tex]\(H_0: \sigma=13\)[/tex]
H. [tex]\(H_0 \quad \sigma \geq 13\)[/tex]
I. [tex]\(H_0: \sigma=13\)[/tex]
The correct statement of hypotheses is:
[tex]\[ H_0: \sigma = 13 \][/tex]
[tex]\[ H_a: \sigma \neq 13 \][/tex]
Based on the given choices, the correct hypothesis pair is stated in choice A:
[tex]\[ A. \, H_0: \sigma = 13 \][/tex]
Therefore, the correct answer is:
[tex]\[ A \][/tex]
Given the claim:
[tex]\[\sigma = 13\][/tex]
First, we need to find the complement of the claim. The complement of the statement "[tex]\(\sigma = 13\)[/tex]" is "[tex]\(\sigma \neq 13\)[/tex]".
So, the complement is:
[tex]\[\sigma \neq 13\][/tex]
In hypothesis testing, the null hypothesis ([tex]$H_0$[/tex]) typically represents the default or initial claim, and the alternative hypothesis ([tex]$H_a$[/tex]) represents the complement or the opposing outcome.
Thus:
[tex]\[ H_0: \sigma = 13 \][/tex]
[tex]\[ H_a: \sigma \neq 13 \][/tex]
Now we look at the given choices to identify which one correctly states [tex]$H_0$[/tex] and [tex]$H_a$[/tex]:
A. [tex]\(H_0: \sigma=13\)[/tex]
B. [tex]\(H_0: \sigma=13\)[/tex]
C. [tex]\(H_0: \sigma \leq 13 \quad H_a: \sigma < 13 \quad H_a: \sigma \leq 13 \quad H_a: \sigma=13\)[/tex]
D. [tex]\(H_0: \sigma \neq 13\)[/tex]
E. [tex]\(H_0: \sigma=13\)[/tex]
F. [tex]\(H_0: \sigma < 13 \quad H_a: \sigma=13 \quad H_a: \sigma > 13 \quad H_a: \sigma=13\)[/tex]
G. [tex]\(H_0: \sigma=13\)[/tex]
H. [tex]\(H_0 \quad \sigma \geq 13\)[/tex]
I. [tex]\(H_0: \sigma=13\)[/tex]
The correct statement of hypotheses is:
[tex]\[ H_0: \sigma = 13 \][/tex]
[tex]\[ H_a: \sigma \neq 13 \][/tex]
Based on the given choices, the correct hypothesis pair is stated in choice A:
[tex]\[ A. \, H_0: \sigma = 13 \][/tex]
Therefore, the correct answer is:
[tex]\[ A \][/tex]
Answer:This means the null hypothesis is that the standard deviation is 13, and the alternative hypothesis is that the standard deviation is not 13.
Step-by-step explanation:
To represent a statistical hypothesis and its complement based on the given statement, we need to follow the standard practice of defining the null hypothesis (
0
H
0
) and the alternative hypothesis (
H
a
).
Given:
=
13
σ=13
The claim:
≠
13
σ
=13
Complement of the claim:
=
13
σ=13
In hypothesis testing, the null hypothesis (
0
H
0
) is typically the statement of no effect or no difference, and it is the complement of the claim we want to test. The alternative hypothesis (
H
a
) represents the claim or the effect we are testing for.
Given the claim
≠
13
σ
=13:
Null hypothesis (
0
H
0
):
=
13
σ=13
Alternative hypothesis (
H
a
):
≠
13
σ
=13
So, the correct representation is:
A.
0
:
=
13
H
0
:σ=13
B.
:
≠
13
H
a
:σ
=13
