A simple random sample of 31 men from a normally distributed population results in a standard deviation of 8.4 beats per minute. The normal range of pulse rate aduits is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats p minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.

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### Hypothesis Testing for Pulse Rate Standard Deviation

A simple random sample of 31 men from a normally distributed population has a standard deviation of 8.4 beats per minute (bpm). The normal range of pulse rates for adults is typically given as 60 to 100 bpm. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 bpm. Use the sample results with a 0.10 significance level to test the hypothesis that the pulse rates of men have a standard deviation equal to 10 bpm. Complete parts (a) through (d) below.

#### a. Identify the null and alternative hypotheses. Choose the correct answer below.

- **Option A**: 
  - \( H_0: \sigma = 10 \) beats per minute
  - \( H_1: \sigma < 10 \) beats per minute

- **Option B**: 
  - \( H_0: \sigma \neq 10 \) beats per minute
  - \( H_1: \sigma = 10 \) beats per minute

- **Option C**:
  - \( H_0: \sigma = 10 \) beats per minute
  - \( H_1: \sigma \neq 10 \) beats per minute
  
- **Option D**: 
  - \( H_0: \sigma \geq 10 \) beats per minute
  - \( H_1: \sigma < 10 \) beats per minute

**Selected Answer:**
The correct null and alternative hypotheses are:
  
**Option C**: 
  - \( H_0: \sigma = 10 \) beats per minute
  - \( H_1: \sigma \neq 10 \) beats per minute
Transcribed Image Text:### Hypothesis Testing for Pulse Rate Standard Deviation A simple random sample of 31 men from a normally distributed population has a standard deviation of 8.4 beats per minute (bpm). The normal range of pulse rates for adults is typically given as 60 to 100 bpm. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 bpm. Use the sample results with a 0.10 significance level to test the hypothesis that the pulse rates of men have a standard deviation equal to 10 bpm. Complete parts (a) through (d) below. #### a. Identify the null and alternative hypotheses. Choose the correct answer below. - **Option A**: - \( H_0: \sigma = 10 \) beats per minute - \( H_1: \sigma < 10 \) beats per minute - **Option B**: - \( H_0: \sigma \neq 10 \) beats per minute - \( H_1: \sigma = 10 \) beats per minute - **Option C**: - \( H_0: \sigma = 10 \) beats per minute - \( H_1: \sigma \neq 10 \) beats per minute - **Option D**: - \( H_0: \sigma \geq 10 \) beats per minute - \( H_1: \sigma < 10 \) beats per minute **Selected Answer:** The correct null and alternative hypotheses are: **Option C**: - \( H_0: \sigma = 10 \) beats per minute - \( H_1: \sigma \neq 10 \) beats per minute
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