MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Title: Investigating the Physiological Changes During Laughter**
**Introduction:**
Researchers conducted a study to explore the physiological changes that accompany laughter. In this investigation, ninety subjects, aged between 18 and 34 years, watched film clips designed to evoke laughter. The researchers measured the heart rate (beats per minute) of each subject during the laughing period. The summary results are as follows: the average heart rate \( \bar{x} = 73.7 \) beats per minute with a standard deviation \( s = 4 \) beats per minute. It is well known that the mean resting heart rate of adults is 71 beats per minute. The goal is to determine whether the true mean heart rate during laughter exceeds 71 beats per minute.
**Hypothesis Testing:**
a. **Setup of Hypotheses:**
We need to test the null hypothesis (\( H_0 \)) against the alternative hypothesis (\( H_a \)) for the given problem.
1. \( H_0: \mu = 71 \)
2. \( H_a: \mu > 71 \)
**Correct Selection:**
\[
\text{C. } H_0: \mu = 71 \\
\text{H_a: } \mu > 71
\]
b. **Rejection Region:**
If the significance level \( \alpha = 0.01 \), determine the rejection region for the test.
**Available Choices:**
- A: \( z < -2.33 \)
- B: \( z < -2.575 \)
- C: \( z > 2.575 \)
- D: \( z > 2.575 \text{ or } z < -2.575 \)
- E: \( z > 2.33 \)
- F: \( z > 2.33 \text{ or } z < -2.33 \)
**Correct Selection:**
\[
\text{E. } z > 2.33
\]
c. **Value of the Test Statistic:**
Calculate the z-value for the test statistic. The formula for the z-value is:
\[
z = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
where](https://content.bartleby.com/qna-images/question/0d0fca7b-87e2-42be-9458-260269753889/4de36ec8-4d5d-49f4-b26f-b64f0632f1ae/x744cme_processed.jpeg)
Transcribed Image Text:**Title: Investigating the Physiological Changes During Laughter**
**Introduction:**
Researchers conducted a study to explore the physiological changes that accompany laughter. In this investigation, ninety subjects, aged between 18 and 34 years, watched film clips designed to evoke laughter. The researchers measured the heart rate (beats per minute) of each subject during the laughing period. The summary results are as follows: the average heart rate \( \bar{x} = 73.7 \) beats per minute with a standard deviation \( s = 4 \) beats per minute. It is well known that the mean resting heart rate of adults is 71 beats per minute. The goal is to determine whether the true mean heart rate during laughter exceeds 71 beats per minute.
**Hypothesis Testing:**
a. **Setup of Hypotheses:**
We need to test the null hypothesis (\( H_0 \)) against the alternative hypothesis (\( H_a \)) for the given problem.
1. \( H_0: \mu = 71 \)
2. \( H_a: \mu > 71 \)
**Correct Selection:**
\[
\text{C. } H_0: \mu = 71 \\
\text{H_a: } \mu > 71
\]
b. **Rejection Region:**
If the significance level \( \alpha = 0.01 \), determine the rejection region for the test.
**Available Choices:**
- A: \( z < -2.33 \)
- B: \( z < -2.575 \)
- C: \( z > 2.575 \)
- D: \( z > 2.575 \text{ or } z < -2.575 \)
- E: \( z > 2.33 \)
- F: \( z > 2.33 \text{ or } z < -2.33 \)
**Correct Selection:**
\[
\text{E. } z > 2.33
\]
c. **Value of the Test Statistic:**
Calculate the z-value for the test statistic. The formula for the z-value is:
\[
z = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
where
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