28) When the binomial test returns a P-value less than 0.05, that generally means that the data match the expectations arising from using the binomial distribution to model the population. True False 29) True or False: If the 95% confidence interval for the proportion does not include the value hypothesized in the binomial test, then the test will almost certainly return a P-value greater than 0.05. Explain your answer. 30) Give an example of outcomes that you would use to conduct a binomial test (do not use examples from the lecture slides - come up with something on your own For the rest of the exam, you will be using the following research information and R to answer questions 36-41. Research information: Researchers tested whether the hot chemical spray ejected by Bombadier beetles when attacked caused predator toads to spit out the beetle. Toads were expected to eat ALL of the beetles if the chemical spray does not deter them. In a sample of 31 beetles, 12 beetles were spit out. 36) In R, the dbinom() function (from the binom package) calculates the Pr[X successes] value. It requires 3 pieces of information: the X value, the n value, and the prob (or po) value. What is the po value for this experiment? 0 0.39 12 31 37) Now use the dbinom() function to calculate the probability that toads spit out exactly 12 of the 31 beetles. Make sure you have the binom package installed: install.packages("binom") Make sure you have the binom package loaded: library(binom) dbinom code: dbinom(x = , size = , prob = ) Probability:Step 3 - 1 point Step 4 (remember to explain what this means biologically) - 2 points 19) Given the following statements, correctly identify whether each statement describes a Type I, Type II, both types, or neither type of error. a) As sample size decreases, the error rate decreases. Type I Type II Both types Neither type b) The true frequency of elm and oak seeds did differ from one another in the soils associated with question 21, but the researchers failed to reject the null hypothesis. Type I Type II Both types Neither type c) If the significance level is a = 0.01, then the error rate for all sample sizes is 0.01. Type I Type II Both types Neither type 20) Which of the following is/are correct assumptions of the binomial test? [Choose all correct answers] The probability of success is the same in every trial The probability of success is less than 0.05 The number of trials is fixed All trials are dependent of each other 21) In a sample of American robins, researchers collected 300 birds, 125 of which were adults and 175 were juveniles. What is the estimated proportion of adults?A P-value smaller than 0.05 and we fail to reject the null hypothesis. A P-value smaller than 0.05 and we reject the null hypothesis. 14) The value of the significance level is the probability of making a Type II error. True False 15) Explain what is wrong with the following statement. In your explanation, be sure to include something about Type I or Type II errors "If a one-sided test rejects the null hypothesis, then a two-sided test would have rejected the null hypothesis as well." 16) Nonsignificant tests are uninformative. True False 17) Describe the relationship between the P-value of a two-sided statistical test and the confidence interval around the value listed in the null hypothesis. 18) Use the following information to complete the 4 steps of hypothesis testing. For each step, write what the step is and then explain that step as it relates to the study listed below. A group of ecologists collected soil samples at three research sites. They wanted to determine if the proportion of oak seeds in the soil samples differed from the proportion of elm seeds. On average, 38% of seeds in the soil samples were oak seeds compared to 62% of elm seeds. The researchers expected similar frequencies between the oak and elm seeds. They determined that there is a 7% chance of finding oak seeds at a 0.38 proportion if their expectation of even frequencies was true. Step 1 (be sure to include the po value in your statements for this test) - 3 points Step 2 (which tree type you treat as your successes does not matter; assume the total sample size was 100) - 1 point22) Consider a sample of 7 robins, assuming that the prevalence of adult robins is 60%. Assuming the binomial distribution is appropriate, what is the probability that exactly 2 of the robins are adults? 23) The value of 5! / 8! Is which of the following? 0.0030 336 1300 14630 24) What is the standard deviation of the proportion when the sample size is 30 values, and the sample proportion is 0.3? 25) What is the standard error of the proportion when the sample size is 30 and the sample proportion is 0.3? 0.007 0.084 0.21 0.458 26) What is the 95% confidence interval, using the Agresti-Coull method, for the proportion when there are 7 observed successes out of a total of 50 trials? 0.014