Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 161 adult males, the mean pulse rate is 67.6 bpm and the standard deviation is 11.1 bpm. Complete parts (a) and (b) below. a. Express the original claim in symbolic form. V bpm (Type an integer or a decimal. Do not round.) b. Identify the null and alternative hypotheses. Họ: bpm bpm (Type integers or decimals. Do not round.) H,:

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### Hypothesis Testing Example: Mean Pulse Rate of Adult Males

**Claim:** The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 161 adult males, the mean pulse rate is 67.6 bpm and the standard deviation is 11.1 bpm. Complete parts (a) and (b) below.

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

\[ 
\mu = 69 \text{ bpm}
\]
*(Type an integer or a decimal. Do not round.)*

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

\[
H_0: \mu = 69 \text{ bpm}
\]

\[
H_1: \mu \neq 69 \text{ bpm}
\]
*(Type integers or decimals. Do not round.)*

### Explanation

**Part (a):** The original claim is that the mean pulse rate of adult males is exactly 69 bpm. In symbolic form, this is represented as \(\mu = 69\) bpm, where \(\mu\) is the population mean.

**Part (b):** The null hypothesis (\(H_0\)) represents the claim to be tested and is usually a statement of no effect or no difference. In this case, it states that the mean pulse rate is 69 bpm. The alternative hypothesis (\(H_1\)) is what you want to prove, which is that the mean pulse rate is different from 69 bpm. This is a two-tailed test since the claim is that the mean is equal to 69, not less than or greater than 69.
Transcribed Image Text:### Hypothesis Testing Example: Mean Pulse Rate of Adult Males **Claim:** The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 161 adult males, the mean pulse rate is 67.6 bpm and the standard deviation is 11.1 bpm. Complete parts (a) and (b) below. #### a. Express the original claim in symbolic form. \[ \mu = 69 \text{ bpm} \] *(Type an integer or a decimal. Do not round.)* #### b. Identify the null and alternative hypotheses. \[ H_0: \mu = 69 \text{ bpm} \] \[ H_1: \mu \neq 69 \text{ bpm} \] *(Type integers or decimals. Do not round.)* ### Explanation **Part (a):** The original claim is that the mean pulse rate of adult males is exactly 69 bpm. In symbolic form, this is represented as \(\mu = 69\) bpm, where \(\mu\) is the population mean. **Part (b):** The null hypothesis (\(H_0\)) represents the claim to be tested and is usually a statement of no effect or no difference. In this case, it states that the mean pulse rate is 69 bpm. The alternative hypothesis (\(H_1\)) is what you want to prove, which is that the mean pulse rate is different from 69 bpm. This is a two-tailed test since the claim is that the mean is equal to 69, not less than or greater than 69.
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