### 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

See similar textbooks

Similar questions

B. Identify the test statistic test C. Identify the P-value for this hypothesis test D. If P-value is reject H0 or fail to reject H0?
The test statistic of z = 0.54 is obtained when testing the claim that p > 0.5. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. Find the P-value. Using a significance level of a = 0.05, should we reject Ho or should we fail to reject Ho?
Test the claim that the proportion of men who own cats is larger than 20% at the .01 significance level. The null and alternative hypothesis would be: Ho: P 0.2 Hop 0.2 Hoμ = 0.2 H₁: p0.2 H₁ : μ 0.2 (to 2 decimals) (to 2 decimals) Ho: p = 0.2 0 H₁: p < 0.2
Prof. Johnson conducts a hypothesis test on whether the proportion of all UBC students who bike to school (denoted as p) equals 30%. Specifically, Prof.Johnson has H, : p = 0.3 versus HA :p+ 0.3. He obtains a P-value of 0.01. On the other hand, Prof. Smith would like to test if there is sufficient evidence to support that p is greater than 0.3 at the 10% significance level. Based on Prof. Johnson's result, will the null hypothesis of Prof. Smith's test be rejected? O A. Yes. O B. No. O C. There is insufficient information to tell.
I
A psychiatrist hypothesized that patients with schizophrenia who have been in the hospital the longest would score the lowest on a mental orientation test. She collected data for six patients with schizophrenia, which are listed in the table below: Years of Hospitalization Mental Orientation 6 7 12 3 5 3 8 Test the hypothesis at the 5% significance level (a = 0.05) using the 5-step hypothesis testing procedure (show ALL steps). Make sure to clearly state the null and alternative hypotheses in formal symbol notation (or in words if formal symbol notation is not appropriate). Show your work. Show the formula and all steps of the calculations and not just the final answer. Round all values to 2 decimal places. If ANOVA is the appropriate test, you must show the complete ANOVA summary table. 7
An institute conducted a clinical trial of its methods for gender selection. The results showed that 153 of 276 babies born to parents using a specific gender-selection method were boys. Use the sign test and a 0.05 significance level to test the claim that the method has no effect on the likelihood of a boy. Let p denote the population proportion of baby boys. Ignore the possibility of the method decreasing the likelihood of a boy. What are the null and alternative hypotheses? O A. Ho: p=0.5 H₂₁: p20.5 O C. Ho: p=0.5 H₁: p=0.5 O B. Ho:p>0.5 H₁: p=0.5 O D. Ho: p=0.5 H₁: p > 0.5 Find the test statistic. Test statistic = Find the P-value. P-value = (Round to four decimal places as needed.) Determine the proper conclusion. Choose the correct answers below. Since the P-value is (Round to two decimal places as needed.) than the significance level, evidence that the method used is effective in increasing the likelihood of a boy. the null hypothesis. There is
B. Identify the test statistic test C. Identify the P-value for this hypothesis test D. If P-value is reject H0 or fail to reject H0?
Prof. Johnson conducts a hypothesis test on whether the proportion of all UBC students who bike to school (denoted as p) equals 30%. Specifically, Prof.Johnson has H0:p=0.3 versus HA:p≠0.3. He obtains a P-value of 0.01. On the other hand, Prof. Smith would like to test if there is sufficient evidence to support that p is greater than 0.3 at the 10% significance level. Based on Prof. Johnson's result, will the null hypothesis of Prof. Smith's test be rejected? A. There is insufficient information to tell.B. Yes.C. No.
2. A study was conducted to examine the difference between the older and younger adult teachers on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 50) and ten younger adults (between 20 and 40) were given a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction, low scores indicative of low life satisfaction. Result of the analysis is presented below. Older Adults Younger Adults Мean 44.5 28.1 Variance 75.38888889 72.98888889 Observations Hypothesized Mean Difference 10 10 df 18 x Stat P(X<=x) one-tail Critical one-tail P(X<=x) two-tail 4.257546666 0.000236832 1.734063607 0.000473663 x Critical two-tail 2.10092204 5. Is there a significant difference between the two groups? 6. Make a writeup of the result using APA format
Two types of medication for hives are being tested to determine if there is a difference in the props of adult patient reactions. 20 out of 200 adults given medication A still have hives after 30 minutes. 12 out of 180 adults given medication B still have hives after 30 minutes. Significance level is a=0.1 1. State the null hypothesis as a complete sentence.
Assume that you plan to use a significance level of α= 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test. A random sampling of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 19 National and 11 American League pitchers had E.R.A's below 3.5.