Statistics Midterm 1 Exam: Data Analysis and Probability - Prof. Cecile M. Ane, Assignments of Data Analysis & Statistical Methods

Download Statistics Midterm 1 Exam: Data Analysis and Probability - Prof. Cecile M. Ane and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity! Stat./For./Hort. 571 Larget and Zhu October 11, 2005 Midterm 1 Name: Please indicate the sections that you attend. Lecture: (circle one) Bret Larget Jun Zhu Discussion: (circle one) Sang-Hoon Cho Xiwen Ma Tao Yu Instructions: 1. The exam is open book. You may use the Course Notes, other texts, lecture notes, homework solutions, your notes, and a calculator. You may not use a laptop computer. 2. Do all your work in the spaces provided. If you need additional space, use the back of the preceding page, indicating clearly that you have done so. 3. To receive full credit, you must show your work. We will award partial credit. 4. Use your time wisely. Do not dwell too long on any one question. Answer as many questions as you can in the time allowed. 5. Note that some questions have multiple parts. For some questions, these parts are independent, so you can work on part (b) or (c) separately from part (a). For graders’ use. Question Possible Points Score 1 20 2 20 3 20 4 20 5 20 Total 100 1. Researchers studying the effects of pollution on biodiversity along rivers gathered data to compare the Black River and the Vermilion River. The reserchers selected at random several 50m by 20m plots along each river and counted the number of species of trees found in each plot. The data from the Vermillion River is shown here. Site n Counts Vermillion 13 8, 9, 9, 9, 9, 10, 11, 12, 13, 13, 13, 13, 16 The researchers collected data from 9 plots on the Black River. The following plot compares data from the two rivers. ● left right 5 10 15 20 (a) Find the median and the first and third quartiles (0.25 and 0.75 sample quantiles) of the Vermillion River measurements. (b) Is the Vermillion River data displayed in the left or right box plot? (c) The standard deviation of the Vermillion River data is 2.4 species. Without any calculation, is the standard deviation of the Black River data less than or greater than the Vermillion River data? Briefly explain. 4. Two rabbits Flopsy and Peter might be found in a garden. At a certain time, the probability is 0.3 that Flopsy is in the garden, the probability is 0.8 that Peter is in the garden, and the probability is 0.2 that neither rabbit is in the garden. (The rabbits may not behave independently. A Venn diagram may be helpful.) (a) What is the probability that both Peter and Flopsy are in the garden? (b) Given that Flopsy is in the garden, what is the probability that Peter is also in the garden? (c) Let Y be the number of these two rabbits in the garden. Find E(Y ). 5. Each of the following settings describes a random variable. For parts (a) and (b), if it is reasonable to model the random variable with a binomial distribution, say so and identify the parameters n and p. If not, briefly explain why. For parts (c) and (d), if it is reasonable to model the random variable with a normal distribution, say so and identify the mean µ and variance σ of the distribution. If not, briefly explain why. (a) One mouse population has 5% mutants. A second mouse population has 10% mutants. A random sample of mice includes forty individuals sampled from the first population and sixty individuals sampled from the second population. The random variable X1 is the number of mutants in the sample. (b) In a forest, 15% of the trees of a certain species have a specific disease. The disease is transmitted by crawling insects and is likely to disperse to neighboring trees. Researchers pick a random location in the forest and sample all trees of the given species within a given radius finding 12 such trees. The random variable X2 is the number sampled trees with the disease. (c) Heights of a species of plant after two months growth in controlled conditions have a non-normal distribution characterized by a moderate amount of right skewness. The mean and standard deviation of this distribution are 40cm and 8cm respec- tively. The random variable X3 is the average height in a random sample of 4 plants from this population. (d) The random variable X4 is the average height of a random sample of 1600 plants from the population described in (c).