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 = 100 alligators, 78 moved toward the underwater sound. Complete parts a through e below. C... a. Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance. Let p be the true proportion of alligators that move toward the underwater sound. Choose the correct answer below. OA. Ho: p>0.50 vs. H₂: p=0.50 OC. Ho: p<0.50 vs. H₂: p=0.50 O E. Ho: p=0.50 vs. Ha: p0.50 O B. Ho: p=0.50 vs. H₂: p<0.50 O D. Ho: p0.50 vs. H₂: p=0.50 OF. Ho: p=0.50 vs. H₂: p>0.50 b. In a sample of n = 100 alligators, assume that 78 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound. (Round to two decimal places as needed.) c. Compute the test statistic for this study. (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.) e. Make the appropriate conclusion in the words of the problem. Test using a = 0.01. OA. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of alligators that move toward the underwater sound is higher
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 = 100 alligators, 78 moved toward the underwater sound. Complete parts a through e below. C... a. Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance. Let p be the true proportion of alligators that move toward the underwater sound. Choose the correct answer below. OA. Ho: p>0.50 vs. H₂: p=0.50 OC. Ho: p<0.50 vs. H₂: p=0.50 O E. Ho: p=0.50 vs. Ha: p0.50 O B. Ho: p=0.50 vs. H₂: p<0.50 O D. Ho: p0.50 vs. H₂: p=0.50 OF. Ho: p=0.50 vs. H₂: p>0.50 b. In a sample of n = 100 alligators, assume that 78 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound. (Round to two decimal places as needed.) c. Compute the test statistic for this study. (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.) e. Make the appropriate conclusion in the words of the problem. Test using a = 0.01. OA. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of alligators that move toward the underwater sound is higher
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 97E
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![## Research on Alligator Movement Response to Underwater Sound
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 = 100 alligators, 78 moved toward the underwater sound. Complete parts a through e below.
### a. Hypothesis Testing
**Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance. Let p be the true proportion of alligators that move toward the underwater sound. Choose the correct answer below.**
- A. \(H_0: p > 0.50 vs. H_a: p = 0.50\)
- B. \(H_0: p = 0.50 vs. H_a: p < 0.50\)
- C. \(H_0: p < 0.50 vs. H_a: p = 0.50\)
- D. \(H_0: p ≠ 0.50 vs. H_a: p = 0.50\)
- E. \(H_0: p = 0.50 vs. H_a: p ≠ 0.50\)
- F. \(H_0: p = 0.50 vs. H_a: p > 0.50\) (Correct answer)
### b. Estimate of True Proportion
**In a sample of n = 100 alligators, assume that 78 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound.**
- (Round to two decimal places as needed.)
\[ \hat{p} = \frac{78}{100} = 0.78 \]
### c. Test Statistic
**Compute the test statistic for this study.**
- (Round to two decimal places as needed.)
\[
z =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50bba9ff-e92f-418a-953f-7454e9aa5e30%2F6305d895-f5cb-42e4-906a-ab534d7b5fec%2F0df14aq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Research on Alligator Movement Response to Underwater Sound
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 = 100 alligators, 78 moved toward the underwater sound. Complete parts a through e below.
### a. Hypothesis Testing
**Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance. Let p be the true proportion of alligators that move toward the underwater sound. Choose the correct answer below.**
- A. \(H_0: p > 0.50 vs. H_a: p = 0.50\)
- B. \(H_0: p = 0.50 vs. H_a: p < 0.50\)
- C. \(H_0: p < 0.50 vs. H_a: p = 0.50\)
- D. \(H_0: p ≠ 0.50 vs. H_a: p = 0.50\)
- E. \(H_0: p = 0.50 vs. H_a: p ≠ 0.50\)
- F. \(H_0: p = 0.50 vs. H_a: p > 0.50\) (Correct answer)
### b. Estimate of True Proportion
**In a sample of n = 100 alligators, assume that 78 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound.**
- (Round to two decimal places as needed.)
\[ \hat{p} = \frac{78}{100} = 0.78 \]
### c. Test Statistic
**Compute the test statistic for this study.**
- (Round to two decimal places as needed.)
\[
z =
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