### Hypothesis Testing ExampleThe federal government is conducting a study to test a hypothesis concerning the average age of men and women filing for Social Security. The specific hypothesis states that the average age of men filing is smaller than the average age of women. To correctly test this hypothesis, we need to establish our null (H₀) and alternative (H₁) hypotheses.**Hypotheses Options:**1. **Option 1:** - $ H_0: \mu_{Men} = \mu_{Women} $ - $ H_1: \mu_{Men} \neq \mu_{Women} $2. **Option 2:** - None of these3. **Option 3:** - $ H_0: \mu_{Men} = \mu_{Women} $ - $ H_1: \mu_{Men} > \mu_{Women} $4. **Option 4:** - $ H_0: \mu_{Men} = \mu_{Women} $ - $ H_1: \mu_{Men} < \mu_{Women} $The correct hypotheses for this study are:- **Null Hypothesis ($ H_0 $)**: The average age of men filing for Social Security is equal to the average age of women. $ H_0: \mu_{Men} = \mu_{Women} $- **Alternative Hypothesis ($ H_1 $)**: The average age of men filing for Social Security is smaller than the average age of women. $ H_1: \mu_{Men} < \mu_{Women} $This is represented by Option 4, which is selected.By establishing these hypotheses, the federal government can conduct appropriate statistical tests to determine if there is sufficient evidence to support the claim that the average age of men filing is indeed smaller than that of women.

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Answered: The federal government would like to…

The federal government would like to test the hypothesis that the average age of men filing for Social Security is smaller than the average age of women. Select the correct hypotheses.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

### Hypothesis Testing Example

The federal government is conducting a study to test a hypothesis concerning the average age of men and women filing for Social Security. The specific hypothesis states that the average age of men filing is smaller than the average age of women. To correctly test this hypothesis, we need to establish our null (H₀) and alternative (H₁) hypotheses.

**Hypotheses Options:**

1. **Option 1:**
- $ H_0: \mu_{Men} = \mu_{Women} $
- $ H_1: \mu_{Men} \neq \mu_{Women} $

2. **Option 2:**
- None of these

3. **Option 3:**
- $ H_0: \mu_{Men} = \mu_{Women} $
- $ H_1: \mu_{Men} > \mu_{Women} $

4. **Option 4:**
- $ H_0: \mu_{Men} = \mu_{Women} $
- $ H_1: \mu_{Men} < \mu_{Women} $

The correct hypotheses for this study are:

- **Null Hypothesis ($ H_0 $)**:
The average age of men filing for Social Security is equal to the average age of women.
$ H_0: \mu_{Men} = \mu_{Women} $

- **Alternative Hypothesis ($ H_1 $)**:
The average age of men filing for Social Security is smaller than the average age of women.
$ H_1: \mu_{Men} < \mu_{Women} $

This is represented by Option 4, which is selected.

By establishing these hypotheses, the federal government can conduct appropriate statistical tests to determine if there is sufficient evidence to support the claim that the average age of men filing is indeed smaller than that of women.

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