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 pointsChapter 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?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)