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

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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.
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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