### Dolphin Communication StudyIn a famous study conducted in the 1960s, two dolphins, Doris and Buzz, were trained to work together to earn fish. Here is how the study was set up:- **Task Description**: Doris was shown an underwater light. Buzz, on the other side of the tank, had to press a button to receive fish: - **Steady Light**: Buzz needed to press a button on the right. - **Blinking Light**: Buzz needed to press a button on the left.At one point, researchers hung a canvas in the middle of the tank to obscure Buzz’s view of the light. After observing the light, Doris swam near the curtain and began to whistle loudly. Shortly after, Buzz whistled back and then correctly pressed the appropriate button. This sequence of events was well-documented by Tintle, Rossman, and Chance in an MAA Prep Workshop.### Observations and DataThe success rate was quite remarkable. Out of 16 trials, Buzz correctly pressed the appropriate button 15 times.### Analyzing the Possibility of CommunicationThere remains a question about whether this successful communication was mere chance. Thus, we need to test the likelihood of the second dolphin, Buzz, achieving this success by random chance alone. Here is how to proceed:1. **Construct Hypotheses**: - **Null Hypothesis (H_0)**: The success was just a lucky streak. Over time, Buzz would get it right around half the time. - **Alternative Hypothesis (H_1)**: Doris effectively communicated to Buzz which button to push, indicating genuine inter-dolphin communication.### Activity Question**Choose the null (H_0) and alternative (H_1) hypotheses you would use to make a claim about the number of times the correct button was selected if you believed they were communicating.**Engage in discussion and think critically about these hypotheses to determine the probability and significance of the observed results. ### Hypothesis Testing ExampleIn hypothesis testing, we often encounter null and alternative hypotheses that we need to test against the data. Below are several hypothesis pairs with one of them selected. These pairs are critical for determining the statistical significance of an experiment.1. **Option 1:** - \( H_0: p = 0.5 \) and \( H_1: p > 0.5 \) *This option suggests that the null hypothesis ( \( H_0 \)) states the probability \( p \) equals 0.5, while the alternative hypothesis ( \( H_1 \)) states \( p \) is greater than 0.5.*2. **Option 2 (Selected):** - \( H_0: p = 0.5 \) and \( H_1: p < 0.5 \) *This option suggests that the null hypothesis ( \( H_0 \)) states the probability \( p \) equals 0.5, while the alternative hypothesis ( \( H_1 \)) states \( p \) is less than 0.5. This option is currently selected.*3. **Option 3:** - \( H_0: p = 0.94 \) and \( H_1: p > 0.94 \) *This option suggests that the null hypothesis ( \( H_0 \)) states the probability \( p \) equals 0.94, while the alternative hypothesis ( \( H_1 \)) states \( p \) is greater than 0.94.*4. **Option 4:** - \( H_0: p = 0.94 \) and \( H_1: p < 0.94 \) *This option suggests that the null hypothesis ( \( H_0 \)) states the probability \( p \) equals 0.94, while the alternative hypothesis ( \( H_1 \)) states \( p \) is less than 0.94.* Understanding these hypothesis pairs is crucial in making data-driven decisions and interpreting the results of statistical tests correctly.

In the given case if we are comparing whether the correct selections by the dolphins were just…

In 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 "swam 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. 1. Construct hypotheses. In this case, two possible explanations are either a) this was just a lucky streak. In the long run Buzz would really get it right about half the time. Or b) Doris really was able to tell Buzz which button to push. Choose the null (H_0) and alternative (H_1) hypothesis you could use to make a claim about the number of times the correct button was selected if you believed they were communicating.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P