b. Change the values in the code so that the output tells you the probability of getting 6 individuals that are not vancomycin-resistant. Explain what is happening in this code (so why does multiplying 0.7 not give you the same value). 1 point c. Produce a graph illustrating the probability distribution of the number of vancomycin-resistant isolates when seven isolates are randomly sampled from the U.S. hospital Enterococcus population. What is the probability that five or more of the isolates are resistant to vancomycin according to your figure? 2 points d. Produce another probability distribution figure as in part c, but now change the number of isolates from 7. Compare and contrast the figures and include an image of both figures somewhere below. 2 pointsThe researchers tested this in two species of newts, Lissotriton vulgaris and L. helveticus. Here are the results: L. vulgaris: X= 50.7, s = 87.3, n = 23, P = 0.011, 95% CI 12.9 -88.4 L. helveticus: X= 199.8, s = 587.0, n = 25, P = 0.102, 95% CI -42.5-442.1 Separately for L. vulargis and L. helveticus, state whether the statistical results provide evidence to reject the null hypothesis. Explain. b. How is the information provided by the P-value different than that provided by the 95% CI? How is the information the same? c. How is the information provided by the standard deviation (s) relative to the mean similar to the information provided by the 95% CI? d. Based on the sample sizes, do you have any concerns about Type I or Type II error? Explain.3. The figure below shows the probability density of colony diameters (in mm) in a hypothetical population of Paenibacillus bacteria. The distribution is continuous, so the probability of sampling a colony within some range of diameter values is given by the area under the curve. Numbers next to the curve indicate the area of the region indicated in red. Consider the case in which two colonies are randomly sampled from the probability distribution shown. 2 points total (1/2 point per a, b, c, and d) 0.4 7 0.4 7 0.3 0.14 0.3 - 0.14 Probability density 0.2 0.2 - 0.1 - 0.1 O 8 10 12 14 2 4 6 8 10 12 14 0.4 7 0.47 0.3 - 0.48 0.3 Probability density 0.2 0.2 0.1 - 0.1 - 0.02 o 2 6 8 10 12 14 6 8 10 12 14 Colony diameter (mm) Colony diameter (mm) Whitlock & Schluter, The Analysis of Biological Data, 3e @ 2020 W. H. Freeman and Company a. Are the events "the first diameter is between 4 and 6" and "the second diameter is between 8 and 12" mutually exclusive? Explain. b. Are the events "the first diameter is between 4 and 6" and "the second diameter is between 8 and 12" independent? Explain.c. The risk for facial cleft is equal for babies born to mothers who take folic acid supplements compared with those born to mothers who do not. 6. Imagine that two researchers independently carry out clinical trials to test the same null hypothesis, that COX-2 selective inhibitors (which are used to treat arthritis) have no effect on the risk of cardiac arrest. They use the same population for their study, but one experimenter uses a sample size of 60 participants, whereas the other uses a sample size of 100. Assume that all other aspects of the studies, including significance levels, are the same between the two studies. 2 points. a. Which study has the higher probability of a Type II error, the 60-participant study or the 100- participant study? Explain. b. Which study has the higher probability of a Type I error? Explain. c. Should the tests be one-tailed or two-tailed? Explain. 7. In many animal species, individuals communicate using ultraviolet (UV) signals, such as bright patches of skin or feathers, that are visible to one another but invisible to humans. A research team (Secondi et al. 2012)investigated the role of UV colors as sexual signals in two closely related species of newts, by asking whether females find males of their own species more attractive when UV radiation is present (UV signals can be seen) compared to when UV light is absent (UV light cannot be seen). Each trial consisted of confining a male newt to one end of an aquarium and measuring how much time a female of the same species chose to spendnear the male. Each male was tested under both UV present and UV absent light conditions. (3 points) Ho: Mean difference in time females spent close to males in UV present and UV absent conditions is 0. In other words, females spent equal time with males in UV present and UV absent conditions. HA: Mean difference in time females spent close to males in UV present and UV absent conditions is greater than 0. In other words, females spent more time with males in UV present than UV absent conditions.2:25 Search HW 2 Assignment.pdf . . . Chapter 5: Probability 1. The human genome is composed of the four DNA nucleotides: A, T, G, and C. Some regions of the human genome are extremely G-C rich (i.e., a high proportion of the DNA nucleotides there are guanine and cytosine). Other regions are relatively A-T rich (i.e., a high proportion of the DNA nucleotides there are adenine and thymine). Imagine that you want to compare nucleotide sequences from two regions of the genome. Sixty percent of the nucleotides in the first region are G-C (30% each of guanine and cytosine) and 40% are A-T (20% each of adenine and thymine). The second region has 25% of each of the four nucleotides. 4 points total (2 points for part a and 2 points for part b) a. If you choose a single nucleotide at random from each of the two regions, what is the probability that they are the same nucleotide? Show your calculations, making your answer clear (by highlighting or bolding; if done in R, feel free to screenshot your Code in the box below) b. Assume that nucleotides over a single strand of DNA occur independently within regions and that you randomly sample a three-nucleotide sequence from each of the two regions. What is the chance that these two triplets are the same? Explain how you determined this. 2. A seed randomly blows around a complex habitat. It may land on any of three different soil types: a high-quality soil that gives a 0.8 chance of seed survival, a medium-quality soil that gives a 0.3 chance of survival, and a low-quality soil that gives only a 0.1 chance of survival. These three soil types (high, medium, and low) are present in the habitat in proportions of 30:20:50, respectively. The probability that a seed lands on a particular soil type is proportional to the frequency of that type in the habitat. 4 points total a. Draw a probability tree to determine the probabilities of survival under all possible circumstances. 2 points. You may take a picture and load it into the box, or build your tree as started below: Survive 0.8 High-Quality Soil b. What is the probability of survival of the seed, assuming that it lands? 1 point c. Assume that the seed has a 0.2 chance of dying before it lands in a habitat. What is its overall probability of survival? 1 pointc. What is the probability that the first diameter is between 4 and 6 and the second diameter is between 8 and 12? d. What is the probability that the first diameter is between 8 and 12 or the second diameter is between 10 and 12? Chapter 6: Hypothesis Testing 4. State the most appropriate null and alternative hypotheses for each of the following experiments or observational studies (3 points). a. A test of whether Pygmy mammoths and continental mammoths differ in their mean femur lengths. Null: Alternative: b. An experiment to test whether mean herbivore damage to a genetically modified crop plant differs from that in the related unmodified crop Null: Alternative: 5. Identify whether each of the following is more appropriate as a null hypothesis or an alternative hypothesis. Explain. (2 points) a. Industrial effluents from a factory into the Mississippi River negatively affect the downstream fish densities b. King cheetahs on average run the same speed as standard spotted cheetahs.c. What is the 95% confidence interval for the proportion of trees leaning toward the equator? 10. Juvenile long-tailed tits (Aegithalos caudatus), a European relative of the chickadee, "help" adult birds raise offspring, such as by feeding their nestlings. What is the evolutionary advantage of helping behavior: practice for parenthood; increased changes of inheriting the adults' territory in future; or indirect genetic benefits via increased success of kin? To investigate, Russell and Hatchwell (2001) monitored the behavior of 17 juveniles, each of which lived equidistant from two nests of adult birds. In each case, one nest was parented by a relative of the helper, and the other was parented by non-kin adults. Sixteen of the juveniles helped at the nest of their kin, whereas one helped at the non-kin nest. Do these results provide evidence for preferential helping at the nests of kin? Conduct the appropriate test and interpret the output from the test. 4 points Written Answer: Image of R Code (showing both your code AND the output): Bonus Question: Enterococcus bacteria are part of the normal intestinal flora of humans, but some strains can cause disease. In U.S. hospitals, 30% of pathogenic isolates are resistant to the antibiotic vancomycin (Wenzel 2004). Assume that seven independent pathogenic isolates have been extracted from patients and tested for resistance. Using the following steps, calculate the probability that five or more of the isolates are resistant to vancomycin: a. Determine what the probability of getting 0 vancomycin-resistant isolates is when looking at seven random isolates (1 point).Chapter 7: Analyzing Proportions 8. One classical experiment on ESP (extrasensory perception) tests for the ability of an individual to show telepathy-to read the mind of another individual. This test uses five cards with different designs, all known to both participants. In a trial, the "sender" sees a randomly chosen card and concentrates on its design. The "receiver" attempts to guess the identity of the card. Each of the five cards is equally likely to be chosen, and only one card is the correct answer at any point. 3 points a. Out of 10 trials, a receiver got four cards correct. What is her success rate? What is her expected rate of success, assuming she is only guessing? b. Is her higher actual success rate reliable evidence that the receiver has telepathic abilities? Carry out the appropriate hypothesis test. C. Assume another (extremely hypothetical) individual tried to guess the ESP cards 1000 times and was correct 350 of those times. This is very significantly different from the chance rate, yet the proportion of her successes is lower than the individual in part a. Explain this apparent contradiction. Use the Shinyapps page for the following 3 questions. 9. The Cook pine tree is native to New Caledonia but has been planted as an ornamental in many countries. The trees tend to lean to one side as they grow. Johns et al. (2017) measured the tilt in 256 individual trees around the world. They found that 233 trees leaned toward the equator (in the Northern Hemisphere they lean south, and in the Southern Hemisphere they lean north), whereas 23 leaned away from the equator. 3 points a. What is the best estimate of the proportion of Cook pine trees that lean toward the equator? b. What is the standard error of the stimulate? What does this quantity measure