**Understanding Directional Null Hypotheses**In the context of hypothesis testing, a directional null hypothesis specifies the direction of the expected effect or difference. Below is an example of how a directional null hypothesis may be represented:**Question:** Which of the following is an example of how a directional null hypothesis can be represented?1. $ \mu_0 = \mu_1 $2. $ \mu_0 \geq \mu_1 $3. $ \mu_0 \neq \mu_1 $4. $ \mu_0 > \mu_1 $**Analysis:**- Options 1 and 3 represent a non-directional (two-tailed) hypothesis.- Options 2 and 4 illustrate a directional hypothesis. In particular:- **Option 4** ($ \mu_0 > \mu_1 $) is a clear example of a directional null hypothesis, suggesting that the mean $ \mu_0 $ is greater than the mean $ \mu_1 $. Understanding the distinction between directional and non-directional hypotheses is crucial for determining the appropriate statistical tests to use in research.

Answered: directional which of the following is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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**Understanding Directional Null Hypotheses**

In the context of hypothesis testing, a directional null hypothesis specifies the direction of the expected effect or difference. Below is an example of how a directional null hypothesis may be represented:

**Question:** Which of the following is an example of how a directional null hypothesis can be represented?

1. $ \mu_0 = \mu_1 $
2. $ \mu_0 \geq \mu_1 $
3. $ \mu_0 \neq \mu_1 $
4. $ \mu_0 > \mu_1 $

**Analysis:**

- Options 1 and 3 represent a non-directional (two-tailed) hypothesis.
- Options 2 and 4 illustrate a directional hypothesis.

In particular:
- **Option 4** ($ \mu_0 > \mu_1 $) is a clear example of a directional null hypothesis, suggesting that the mean $ \mu_0 $ is greater than the mean $ \mu_1 $.

Understanding the distinction between directional and non-directional hypotheses is crucial for determining the appropriate statistical tests to use in research.

Expert Solution

Step 1

Hypothesis:

A statistical hypothesis is a claim or assumption about a population parameter or statement, that may or may not be true.

Directional hypothesis:

The directional hypothesis is also known as one-tailed.

$H_{0} : μ_{0} \geq μ_{1}$

$H_{1} : μ_{0} < μ_{1}$

$H_{0} : μ_{0} \leq μ_{1}$

$H_{1} : μ_{0} > μ_{1}$

Non-Directional hypothesis:

The directional hypothesis is also known as one-tailed.

$H_{0} : μ_{0} = μ_{1}$

$H_{1} : μ_{0} \neq μ_{1}$

Hence, The example of the directional null hypothesis is:

$H_{0} : μ_{0} \geq μ_{1}$

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directional which of the following is on example of how a null hypothes can be represented. 1.) M₁ = μ₁ 3.) можли 2. MO > My 4.) мо) MI