Answer all...Dr. Raja Rastami's research group recently published an important paper in a leading physiology journal. Four months after the publication of the manuscript, Dr. Rastami is contacted by a colleague who has been unable to reproduce the results presented in two figures of the paper. Dr. Rastami sends copies of the pertinent laboratory protocols and recipes to her colleague and thinks no more of the discrepancy. Two months later, a graduate student in a competitor's laboratory contacts Dr. Rastami and reports that he, too, was unable to reproduce the results. After this second call, Dr. Rastami meets with Adam Green, the postdoctoral fellow who did the experiments in question. She asks Adam to bring his data book to the meeting so they can review the results together. Once in Dr. Rastami's office, Adam confesses that he has been remiss in keeping his data book. He says that all of his electrophysiology experiments observations were digitally recorded. Adam then transcribed these observations into his data book. However, there was a period of several days when his microphone was not working properly. Although Adam replaced the microphone as soon as he found that it was not working, he relied on his memory to transcribe the results of those particular experiments. After completing the figures for the manuscript, Adam was pleased to find that his data supported Dr. Rastami's hypothesis. Dr. Rastami comes to you for advice on how to handle this situation. What do you suggest?

more. 2. Identifying binomial data Aa Aa A researcher interested in the transition from middle school to high school surveys a random sample of 500 eighth-grade students. Which of the following statistics are computed using binomial data? O The total number of siblings among students in the sample O The schools currently attended by students in the sample O The average distance the students travel from home to school O The proportion who know more than one language Suppose that the researcher wants to conduct a hypothesis test about the proportion of his sample who live with grandparent. For the researcher to appropriately use the normal approximation to the binomial distribution, the proportion of students in the population of eighth-grade students who live with a grandparent must be at least and not greater than Suppose that the actual proportion of students in the population of eighth-grade students who live with a grandparent is 0.15. Then the number of students in a sample of 500 eighth-grade students who live with a grandparent is approximately normal, with mean and standard deviationProblem 4 Markov Chains A camera store stocks a particular model camera that can be ordered weekly. The demand for this camera (the number of units that would be sold if the inventory wasn't depleted) follows a binomial distribution with success probability . Assume that at the end of the week (Saturday night, the store owner reviews his inventory level and orders enough cameras to bring his inventory level back to 3 cameras. (For example, if there is one camera in stock at the end of the week, the owner will order two cameras). The order comes in at the end of the next week (that is aer demand has been realized ). The state of the system is the number of cameras on hand at the end of the week. Example 2.6 (Wright-Fisher model) The Wright-Fisher model describes the evolution of a fixed population of k genes. Genes can be one of two types, called alleles: A or a. Let A,, denote the number of A alleles in the population at time n. where time is measured by generations. Under the model, the number of A alleles at time n + 1 is obtained by drawing with replacement from the gene population at time n. Thus, conditional on there being i alleles of type A at time n, the number of A alleles at time n + I has a binomial distribution with parameters k and p = i/k. This gives a Markov chain with transition matrix defined by Py = ( 1 ) ( # ) ( 1 - 2 ) k-j for 0