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 point7) Based on the probability distribution of bacteria colony diameters in the figure below, which value of colony diameter has the lowest probability of being randomly selected in a sample? 6 mm 8 mm 10 mm 12 mm 0.4 - 0.3 Probability density 0.2 - 0.1 6 8 10 12 14 Colony diameter (mm) 8) A survey of canopy ants in Panama found 120 Cephalotes workers, 40 Pseudomyrmex workers, 30 Crematogaster workers, and 10 Paraponera workers. a) If an ant is randomly chosen from this survey, what is the probability that it will be a Cephalotes ant? 0.05 0.6 5 60 b) If an ant is randomly chosen from this survey, what is the probability that it will be a Pseudomyrmex or Paraponera ant? c) If two ants are randomly chosen from this survey, what is the probability that one will be a Pseudomyrmex ant and the other will be a Paraponera ant?d) If an ant is randomly chosen from the population and then returned to the population (i.e.,the total number of ants is the same across all trials), what is the probability that we will select a Cephalotes, then a Paraponera, and then a Crematogaster worker? 9) Explain how you might make the probability of choosing a Cephalotes, a Paraponera, and then a Crematogaster ant worker from question 8d a dependent, rather than independent, sample. 10) The P-value is the probability that the null hypothesis is true. True False 11) Typically, the null hypothesis is the statement that we are interested in Accepting Disproving Proving Rejecting 12) The sampling distribution for a test statistic if the null hypothesis is true is called which of the following? The hypothetical distribution The null distribution The test distribution The true distribution 13) Consider a situation in which we calculate a 95% confidence interval that ranges from 18 to 23. If we conducted a two-sided test with the null hypothesis of the population mean equaling 17, what would the likely result of our test be? A P-value larger than 0.05 and we fail to reject the null hypothesis. A P-value larger than 0.05 and we reject the null hypothesis.4) A study published in March of 2021 found that COVID-19 antigen tests correctly identified COVID-19 infections in 72% of people with symptoms, compared to 58% of people without symptoms (Dinnes et al. 2021). The tree diagram below shows the possible outcomes with the associated probabilities. Out of all COVID-19 positive individuals, only 41% of individuals are symptomatic (Ma et al. 2021). What is the probability of getting an incorrect test result from an antigen test when you have COVID-19? Give your answer as a decimal precise to two decimal places. COVID-19 Test Result Status for individuals who have the virus 0.72 Positive Sympto- matic 0.41 0.28 Negative Positive 0.58 0.59 Asympto -matic 0.42 Negative 5) Consider the following: In a population of 2 species of trees, 45% of trees are elms and the other 55% of trees are oaks. If 60% of the trees are infected with a disease, which of the following statements is/are correct? Assume that the infection is independent from the tree species. [Choose all correct answers] The probability of randomly selecting an elm tree is 0.45. The probability of randomly selecting an infected tree or an elm tree is 0.78. The probability of randomly selecting an infected tree or an elm tree is 1. The probability of randomly selecting either an oak or elm tree is 1. 6) State whether the following statement is True or False, and explain why or why not: "The addition rule states that Pr[A and B] = Pr[A] + Pr[B]."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