For the following conjecture, state the null and alternative hypotheses. The average resting pulse rate of male marathon runners is greater than 70 beats per minute. The null hypothesis is H: O
For the following conjecture, state the null and alternative hypotheses. The average resting pulse rate of male marathon runners is greater than 70 beats per minute. The null hypothesis is H: O
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Formulating Hypotheses for a Statistical Conjecture
For the following conjecture, state the null and alternative hypotheses:
**Conjecture:** The average resting pulse rate of male marathon runners is greater than 70 beats per minute.
#### Hypotheses
**Null Hypothesis (\( H_0 \))**
The null hypothesis represents the statement we aim to test against. Typically, it denotes no effect or no difference. In this case:
\[ H_0: \mu \leq 70 \]
where \(\mu\) represents the average resting pulse rate of male marathon runners.
**Alternative Hypothesis (\( H_1 \))**
The alternative hypothesis is what we aim to support. It represents a statement which we suspect might be true instead of the null hypothesis. In this case:
\[ H_1: \mu > 70 \]
The symbols needed for constructing these hypotheses are presented in a graphical interface as follows:
- \( < \) (less than)
- \( \leq \) (less than or equal to)
- \( > \) (greater than)
- \( \geq \) (greater than or equal to)
- \( = \) (equal to)
- \( \neq \) (not equal to)
The user is required to select the appropriate symbol from these options to complete the hypotheses accurately.
#### Conclusion
- Null Hypothesis (\( H_0 \)): \[ H_0: \mu \leq 70 \]
- Alternative Hypothesis (\( H_1 \)): \[ H_1: \mu > 70 \]
By formulating these hypotheses, one can perform statistical tests to support or refute the conjecture regarding the average resting pulse rate of male marathon runners.
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This translation should be appropriate for an educational website, providing clarity on how to state and interpret null and alternative hypotheses for a statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02edcb37-a5b4-4ad7-814d-fe9fafc40457%2F61f8680d-95f6-4ea6-b3f1-990625e5bda6%2F5biyf6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Formulating Hypotheses for a Statistical Conjecture
For the following conjecture, state the null and alternative hypotheses:
**Conjecture:** The average resting pulse rate of male marathon runners is greater than 70 beats per minute.
#### Hypotheses
**Null Hypothesis (\( H_0 \))**
The null hypothesis represents the statement we aim to test against. Typically, it denotes no effect or no difference. In this case:
\[ H_0: \mu \leq 70 \]
where \(\mu\) represents the average resting pulse rate of male marathon runners.
**Alternative Hypothesis (\( H_1 \))**
The alternative hypothesis is what we aim to support. It represents a statement which we suspect might be true instead of the null hypothesis. In this case:
\[ H_1: \mu > 70 \]
The symbols needed for constructing these hypotheses are presented in a graphical interface as follows:
- \( < \) (less than)
- \( \leq \) (less than or equal to)
- \( > \) (greater than)
- \( \geq \) (greater than or equal to)
- \( = \) (equal to)
- \( \neq \) (not equal to)
The user is required to select the appropriate symbol from these options to complete the hypotheses accurately.
#### Conclusion
- Null Hypothesis (\( H_0 \)): \[ H_0: \mu \leq 70 \]
- Alternative Hypothesis (\( H_1 \)): \[ H_1: \mu > 70 \]
By formulating these hypotheses, one can perform statistical tests to support or refute the conjecture regarding the average resting pulse rate of male marathon runners.
---
This translation should be appropriate for an educational website, providing clarity on how to state and interpret null and alternative hypotheses for a statistical analysis.
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