Claim: The standard deviation of pulse rates of adult males is more than 12 bpm. For a random sample of 148 adult males, the pulse rates have a standard deviation of 12.9 bpm. Complete parts (a) and (b) below. a. Express the original claim in symbolic form. bpm (Type an integer or a decimal. Do not round.) b. Identify the null and alternative hypotheses. Ho: bpm

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**Claim:** The standard deviation of pulse rates of adult males is more than 12 bpm. For a random sample of 148 adult males, the pulse rates have a standard deviation of 12.9 bpm. Complete parts (a) and (b) below.

**a. Express the original claim in symbolic form.**

(There is a dropdown menu to select symbols and a text box to enter values)
- The input box contains "bpm" and the instruction "Type an integer or a decimal. Do not round."

**b. Identify the null and alternative hypotheses.**

\[ H_0: \]
(There is a dropdown menu to select symbols and a text box to enter values)
- The input box contains "bpm"

---

### Detailed Explanation

**Part (a): Express the original claim in symbolic form**

To express the original claim symbolically, we need to translate the statement "The standard deviation of pulse rates of adult males is more than 12 bpm" into a formal mathematical expression. Usually, the standard deviation is represented by the symbol \( \sigma \). Therefore, the claim can be expressed as:
\[ \sigma > 12 \text{ bpm} \]

**Part (b): Identify the null and alternative hypotheses**

In hypothesis testing, the null hypothesis (\( H_0 \)) typically represents the statement of no effect or no difference. It is the hypothesis that the researcher attempts to disprove. On the other hand, the alternative hypothesis (\( H_a \)) represents the statement that there is an effect or a difference. In this case:

- The null hypothesis \( H_0 \) would state that the standard deviation of pulse rates of adult males is less than or equal to 12 bpm:
  \[ H_0: \sigma \leq 12 \text{ bpm} \]

- The alternative hypothesis \( H_a \) would state that the standard deviation of pulse rates of adult males is more than 12 bpm (this is the original claim):
  \[ H_a: \sigma > 12 \text{ bpm} \]

This setup of hypotheses allows for a one-tailed test to determine if the standard deviation is significantly greater than 12 bpm.
Transcribed Image Text:**Claim:** The standard deviation of pulse rates of adult males is more than 12 bpm. For a random sample of 148 adult males, the pulse rates have a standard deviation of 12.9 bpm. Complete parts (a) and (b) below. **a. Express the original claim in symbolic form.** (There is a dropdown menu to select symbols and a text box to enter values) - The input box contains "bpm" and the instruction "Type an integer or a decimal. Do not round." **b. Identify the null and alternative hypotheses.** \[ H_0: \] (There is a dropdown menu to select symbols and a text box to enter values) - The input box contains "bpm" --- ### Detailed Explanation **Part (a): Express the original claim in symbolic form** To express the original claim symbolically, we need to translate the statement "The standard deviation of pulse rates of adult males is more than 12 bpm" into a formal mathematical expression. Usually, the standard deviation is represented by the symbol \( \sigma \). Therefore, the claim can be expressed as: \[ \sigma > 12 \text{ bpm} \] **Part (b): Identify the null and alternative hypotheses** In hypothesis testing, the null hypothesis (\( H_0 \)) typically represents the statement of no effect or no difference. It is the hypothesis that the researcher attempts to disprove. On the other hand, the alternative hypothesis (\( H_a \)) represents the statement that there is an effect or a difference. In this case: - The null hypothesis \( H_0 \) would state that the standard deviation of pulse rates of adult males is less than or equal to 12 bpm: \[ H_0: \sigma \leq 12 \text{ bpm} \] - The alternative hypothesis \( H_a \) would state that the standard deviation of pulse rates of adult males is more than 12 bpm (this is the original claim): \[ H_a: \sigma > 12 \text{ bpm} \] This setup of hypotheses allows for a one-tailed test to determine if the standard deviation is significantly greater than 12 bpm.
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