8:50 PM quizizz.com Searc Playing a Ga... Paraphrasin... This Is Just... William Carl... Edpuzzle iowa housin.. Home | Hous... and alte... 2/22 Which of the following represents the appropriate null \& alternative hypotheses? The mean height of women is greater than 64" $$ \begin{array}{l} H_{0}: \mu \leq 64^{\prime \prime} \ H_{a}: \mu64^{\prime \prime} \end{array} $$ $$ H_{0}: p64^{\prime \prime} $$ $$ H_{0}: p=64^{\prime \prime} $$ $$ H_{0}: \mu \geq 64^{\prime \prime} $$ $$ H_{a}: p \neq 64^{\prime \prime} $$ $$ H_{a}: \mu \neq 64^{\prime \prime} $$ Emilio Mejia

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8:50 PM quizizz.com Searc Playing a Ga... Paraphrasin... This Is Just... William Carl... Edpuzzle iowa housin.. Home | Hous... and alte... 2/22 Which of the following represents the appropriate null \& alternative hypotheses? The mean height of women is greater than 64" $$ \begin{array}{l} H_{0}: \mu \leq 64^{\prime \prime} \ H_{a}: \mu>64^{\prime \prime} \end{array} $$ $$ H_{0}: p>64^{\prime \prime} $$ $$ H_{0}: p=64^{\prime \prime} $$ $$ H_{0}: \mu \geq 64^{\prime \prime} $$ $$ H_{a}: p \neq 64^{\prime \prime} $$ $$ H_{a}: \mu \neq 64^{\prime \prime} $$ Emilio Mejia

UpStudy AI · Accepted Answer

To determine the appropriate null and alternative hypotheses based on the statement "The mean height of women is greater than 64 inches," we need to define the hypotheses clearly.

1. **Null Hypothesis (H₀)**: This is a statement of no effect or no difference. In this case, it would state that the mean height of women is less than or equal to 64 inches.
   
2. **Alternative Hypothesis (Hₐ)**: This is what we want to prove. In this case, it states that the mean height of women is greater than 64 inches.

Based on this understanding, we can formulate the hypotheses as follows:

- **Null Hypothesis (H₀)**: $$ \mu \leq 64^{\prime\prime} $$
- **Alternative Hypothesis (Hₐ)**: $$ \mu > 64^{\prime\prime} $$

Now, let's analyze the options provided:

1. $$ H_{0}: \mu \leq 64^{\prime\prime} $$ and $$ H_{a}: \mu > 64^{\prime\prime} $$ - This is correct.
2. $$ H_{0}: p > 64^{\prime\prime} $$ - Incorrect, as it uses $$ p $$ instead of $$ \mu $$.
3. $$ H_{0}: p = 64^{\prime\prime} $$ - Incorrect, as it uses $$ p $$ instead of $$ \mu $$.
4. $$ H_{0}: \mu \geq 64^{\prime\prime} $$ - Incorrect, as it does not reflect the "less than or equal to" condition.
5. $$ H_{a}: p \neq 64^{\prime\prime} $$ - Incorrect, as it uses $$ p $$ instead of $$ \mu $$.
6. $$ H_{a}: \mu \neq 64^{\prime\prime} $$ - Incorrect, as it does not reflect the "greater than" condition.

Thus, the correct representation of the null and alternative hypotheses is:

$$
\begin{array}{l}
H_{0}: \mu \leq 64^{\prime\prime} \
H_{a}: \mu > 64^{\prime\prime}
\end{array}
$$
The correct hypotheses are: - **Null Hypothesis (H₀):** The mean height of women is less than or equal to 64 inches ($$ \mu \leq 64^{\prime\prime} $$) - **Alternative Hypothesis (Hₐ):** The mean height of women is greater than 64 inches ($$ \mu > 64^{\prime\prime} $$)

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