Alligators have shown the ability to determine the direction of an airborne sound. But can they locate underwater sounds? This was the subject of a study. Alligators were monitored for movement toward a sound produced from a submerged diving bell. Movements within a 180° arc of the direction toward the sound were scored as movements toward the sound; all movements in other directions were scored as movements away from the sound. Consequently, the researchers assumed that the proportion of movements toward the sound expected by chance is 180 /360° = 0.5. In a sample of n= 50 alligators, 29 moved toward the underwater sound. Complete parts a through e below. proporuon or alligators tnat move towara ne unuerwater souna. CnOose ne correct answer pelow. O A. Ho: p>0.50 vs. Ha: p= 0.50 O B. Ho: p= 0.50 vs. Ha: p<0.50 O C. Ho: p=0.50 vs. Ha: p#0.50 · D. Ho: p=0.50 vs. Ha: p>0.50 O E. Ho: p#0.50 vs. Ha: p= 0.50 OF. Ho: p<0.50 vs. Ha: p= 0.50 b. In a sample of n= 50 alligators, assume that 29 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound. 0.58 (Round to two decimal places as needed.) c. Compute the test statistic for this study. 1.13 (Round to two decimal places as needed.) d. Compute the observed significance level (p-value) of the test. |(Round to three decimal places as needed.)
Alligators have shown the ability to determine the direction of an airborne sound. But can they locate underwater sounds? This was the subject of a study. Alligators were monitored for movement toward a sound produced from a submerged diving bell. Movements within a 180° arc of the direction toward the sound were scored as movements toward the sound; all movements in other directions were scored as movements away from the sound. Consequently, the researchers assumed that the proportion of movements toward the sound expected by chance is 180 /360° = 0.5. In a sample of n= 50 alligators, 29 moved toward the underwater sound. Complete parts a through e below. proporuon or alligators tnat move towara ne unuerwater souna. CnOose ne correct answer pelow. O A. Ho: p>0.50 vs. Ha: p= 0.50 O B. Ho: p= 0.50 vs. Ha: p<0.50 O C. Ho: p=0.50 vs. Ha: p#0.50 · D. Ho: p=0.50 vs. Ha: p>0.50 O E. Ho: p#0.50 vs. Ha: p= 0.50 OF. Ho: p<0.50 vs. Ha: p= 0.50 b. In a sample of n= 50 alligators, assume that 29 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound. 0.58 (Round to two decimal places as needed.) c. Compute the test statistic for this study. 1.13 (Round to two decimal places as needed.) d. Compute the observed significance level (p-value) of the test. |(Round to three decimal places as needed.)
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![### Understanding Alligator Sensory Abilities in Locating Underwater Sounds
#### Study Overview:
Alligators have demonstrated the ability to detect the direction of airborne sounds, but can they also locate underwater sounds? This question was the focus of a study where alligators were observed for movements toward an underwater sound produced by a submerged diving bell. Movements within a 180° arc directed toward the sound were considered as movements toward it, while those in other directions were seen as movements away from the sound. The researchers accordingly hypothesized that the proportion of movements toward the sound expected by random chance is \( \frac{180}{360} = 0.50 \).
In a sample of \( n = 50 \) alligators, 29 showed movement toward the underwater sound.
#### Problem Statements and Steps:
**Hypothesis Testing (Part a):**
Given the scenarios, select the appropriate null and alternative hypotheses consistently with the above observation:
- \(H_0: p = 0.50 \)
- \(H_a: p > 0.50 \)
**Computing Estimates and Test Statistics (Parts b to d):**
1. **Estimate of Proportion (Part b):**
- Compute the sample proportion of alligators that moved toward the underwater sound.
- Given 29 out of 50 moved toward the sound, the estimate is:
\[ \hat{p} = \frac{29}{50} = 0.58 \]
- Result: \( 0.58 \) (rounded to two decimal places)
2. **Test Statistic (Part c):**
- Calculate the test statistic using the formula for a one-sample proportion z-test:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
Where \( \hat{p} = 0.58 \), \( p_0 = 0.50 \), and \( n = 50 \):
\[
z = \frac{0.58 - 0.50}{\sqrt{\frac{0.50 \times 0.50}{50}}} \approx 1.13
\]
- Result: \( 1.13 \) (rounded to two decimal places)
3. **Observed Significance Level (p-value) (Part d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d0fca7b-87e2-42be-9458-260269753889%2F1333b86e-2264-48c5-bab2-9b9d885fda63%2F3o8ega5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Alligator Sensory Abilities in Locating Underwater Sounds
#### Study Overview:
Alligators have demonstrated the ability to detect the direction of airborne sounds, but can they also locate underwater sounds? This question was the focus of a study where alligators were observed for movements toward an underwater sound produced by a submerged diving bell. Movements within a 180° arc directed toward the sound were considered as movements toward it, while those in other directions were seen as movements away from the sound. The researchers accordingly hypothesized that the proportion of movements toward the sound expected by random chance is \( \frac{180}{360} = 0.50 \).
In a sample of \( n = 50 \) alligators, 29 showed movement toward the underwater sound.
#### Problem Statements and Steps:
**Hypothesis Testing (Part a):**
Given the scenarios, select the appropriate null and alternative hypotheses consistently with the above observation:
- \(H_0: p = 0.50 \)
- \(H_a: p > 0.50 \)
**Computing Estimates and Test Statistics (Parts b to d):**
1. **Estimate of Proportion (Part b):**
- Compute the sample proportion of alligators that moved toward the underwater sound.
- Given 29 out of 50 moved toward the sound, the estimate is:
\[ \hat{p} = \frac{29}{50} = 0.58 \]
- Result: \( 0.58 \) (rounded to two decimal places)
2. **Test Statistic (Part c):**
- Calculate the test statistic using the formula for a one-sample proportion z-test:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
Where \( \hat{p} = 0.58 \), \( p_0 = 0.50 \), and \( n = 50 \):
\[
z = \frac{0.58 - 0.50}{\sqrt{\frac{0.50 \times 0.50}{50}}} \approx 1.13
\]
- Result: \( 1.13 \) (rounded to two decimal places)
3. **Observed Significance Level (p-value) (Part d
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