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Statistics 104, Homework 4Due : February 14th, 2018, In ClassThis homework is to practice more on con dence interval and to practice permutation tests. Rcodes need to be attached. Total: 90 points.1. (30 points) Understand con dence interval better through simulations. Suppose you are pro-vided with 25 observations (Y1;Y2;:::;Y25) and are asked to construct the 90% con denceinterval for 0:7, the 70th percentile of the population distribution. Based on Midterm 1, weknow that we would like to use Y(14) and Y(22) to construct the con dence interval. However,there are two other choices that seem also not bad: (Y(12);Y(21)), and (Y(15);Y(24)).Suppose the 25 observations are randomly drawn from a uniform. distribution, U([0,10]), i.e.,the probability density function is f(y) =0:1 0 y 100 otherwise .(a) What is the 70th percentile of U([0;10])?(b) Randomly generate 25 observations from the distribution, construct the three con denceintervals. Repeat it for B = 10;000 times. Among the B con dence intervals based on(Y(14);Y(22)), what is the percentage of intervals covering the true 0:7 you obtained in(a)? Does it ful ll the requirement of 90%? Answer the same questions for intervalsbased on (Y(12);Y(21)), and (Y(15);Y(24)), respectively.(c) For the B intervals based on (Y(14);Y(22)), compute the average length. Do the same forintervals based on (Y(12);Y(21)), and (Y(15);Y(24)). Among the three, which one has thesmallest average length?2. (60 points) Two-sample permutation test. A biologist examined the e ect of a fungal infectionon the eating behavior. of rodents. Among twelve rodents, eight are randomly chosen andprovided with infected apples (Experiment) and the rest four are provided with sterile apples(Control). The amounts consumed (grams of apple/kilogram of body weight) are listed inthe following table.Experimental Group 11, 33, 48, 34, 112, 369, 64, 44Control Group 177, 80, 141, 332Let 1 and 2 be the population mean consumption of the experimental group and controlgroup, respectively. We would like to conduct the hypothesis testH0 : 1 = 2 vsHa : 1 at 0.05 signi cance level. Perform. the permutation test for each of the following six teststatistics. For each test statistic, use R to get the permutation distribution of the statistic,state how the p-value shall be computed, report the exact p-value, and draw your conclusion.(a) Mean di erence of the two groups.(b) Sum of the experimental group.(c) Median di erence of the two groups.(d) Rank the pooled data from both groups and use mean di erence based on the ranks.(e) Rank the pooled data from both groups and use sum of ranks in the experimental group.(f) The Mann-Whitney statistic: the number of pairs (Xi;Yj) for which Xi 1本团队核心人员组成主要包括BAT一线工程师,精通德英语!我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域:window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业,所以值得信赖。如有需要,请加QQ:99515681 或邮箱:[email protected] 微信:codehelp QQ:99515681 或邮箱:[email protected] 微信:codehelp

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