### Dolphin Communication StudyIn a famous study done in the 1960s, two dolphins, Doris and Buzz, were trained to work together to earn fish. Doris was shown a light underwater. If the light was on steadily, her partner Buzz on the other side of the tank needed to press a button on the right for them to earn fish. If the light was blinking, he needed to press a button on the left.At one point in the study, the researcher hung a canvas in the middle of the tank in such a way that Buzz could not see the light. After looking at the light, Doris "swammed near the curtain and began to whistle loudly. Shortly after that Buzz whistled back and then pressed the correct button" (Tintle, Rossman and Chance, MAA Prep Workshop).Of course, getting it right once was not enough to convince the scientists that there was really communication going on. It turned out that in 15 out of 16 trials the dolphin pushed the correct button.Of course, it is possible that this happened just out of random chance—that the second dolphin just happened to hit a lucky streak. We want to try to determine just how unlikely that would be.### Statistical Analysis**Question:**Using a significance level of 0.05, test the claim that the dolphins were communicating with each other that led them to choose the correct button more than 50% of the time. Use the p-value from the previous question to "reject" or "fail to reject" the null hypothesis and state your conclusion.**Help with this question:**- **Null Hypothesis (H0):** The dolphins' success rate in choosing the correct button is 50% or less (no communication).- **Alternative Hypothesis (H1):** The dolphins' success rate in choosing the correct button is more than 50% (communication).To perform this test, you would likely use a binomial test or a z-test for proportions to determine if the observed rate (15 out of 16 trials) is significantly greater than 50%. Based on the p-value calculated, you will either reject or fail to reject the null hypothesis. If the p-value is less than 0.05, you reject the null hypothesis, suggesting that the dolphins were indeed communicating. If the p-value is greater than 0.05, you fail to reject the null hypothesis. **Identify the Correct Interpretation of the P-Value in the Study of Dolphin Communication**### Statements:1. ☐ The P-value is more than 0.05 so we support the claim that the dolphins are communicating. 2. ☑ The P-value is less than 0.05 so we fail to reject the null and accept that the dolphins are communicating. 3. ☐ The P-value is less than 0.05 so we support the claim that the dolphins are communicating. 4. ☑ The P-value is less than 0.05 so reject the null and believe the dolphins are communicating.### Explanation:- The first checkbox beside the statement "The P-value is more than 0.05 so we support the claim that the dolphins are communicating" is empty, indicating that this statement is incorrect.- The second checkbox beside the statement "The P-value is less than 0.05 so we fail to reject the null and accept that the dolphins are communicating" is checked, indicating that this statement is correct according to the given scenario.- The third checkbox beside the statement "The P-value is less than 0.05 so we support the claim that the dolphins are communicating" is empty, indicating that this statement is incorrect.- The fourth checkbox beside the statement "The P-value is less than 0.05 so reject the null and believe the dolphins are communicating" is checked, indicating that this statement is correct according to the given scenario.### Key Concepts:- **P-value**: A measure to determine the significance of the results.- **Null Hypothesis (H₀)**: The default assumption that there is no effect or no difference.- **Alternative Hypothesis (H₁)**: The hypothesis that there is an effect or a difference. In research, if the P-value is less than a predetermined threshold (commonly 0.05), the null hypothesis is rejected, indicating that the results are statistically significant. However, nuances in interpreting these results are vital, hence the need for correct statements.

Answered: Image /qna-images/answer/da8a90b8-5f8f-4531-8577-7bc68bb42770.jpg

5. Using a significance level of 0.05, test the claim that the dolphins were communicating with each other that led them to choose the correct button more than 50% of the time. Use the p- value from the previous question to "reject" or "fail to reject" the null hypothesis and state your conclusion.

5. Using a significance level of 0.05, test the claim that the dolphins were communicating with each other that led them to choose the correct button more than 50% of the time. Use the p- value from the previous question to "reject" or "fail to reject" the null hypothesis and state your conclusion.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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