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Statistics: HW 7Deadline: April 18 at 8 p.m.Problem 1. Suppose we have n data points drawn from a N(μ, 52) distribution, wherethe value of μ is unknown.(a) (1 point) Suppose we have 16 data points and that the sample mean is ˉx = 20.Construct a precise 95% confidence interval for the μ.(b) (1 point) Explain why the confidence interval for the mean when n = 100 is alwaysnarrower than the confidence interval when n = 10.(c) (1 point) What is the smallest value of n so that the 95% confidence interval for themean will have width less than 1.0? (Still with σ2 = 52)Problem 2. Adult mayflies live anywhere from 30 minutes to 1 day, depending on thespecies. Data for one species was collected by tracking 10 mayflies. The recorded lifespansin hours were17.68, 13.69, 11.22, 11.05, 13.86, 14.47, 14.50, 13.47, 10.04, 13.10(a) (1 point) Compute a 95% confidence interval for the mean lifetime of this species ofmayfly.(b) (1 point) What assumptions did you make in part (a)?(c) (1 point) Compute a 95% confidence interval for the standard deviation of distributionof the lifetime of a mayfly.(d) (1 point) Based on the sample variance of this data estimate the number of datapoints you would need to make the width of the 95% confidence interval for themean less than or equal to 1 hour.(e) (1 point) Is the value of n in part (d) guaranteed to be sufficient? Explain yourreasoning.Problem 3. Finish the t-test task from the practice:(a) (4 points) Build the distribution of p-values when H0 is true(b) (8 points) Build the distribution of p-values when H0 is false. Try to decrease thesample size, while holding the mean the same. Try to increase the mean whileholding the sample size the same. Explain your results.(c) (4 points) Build the distribution of p-values when xi ～ Exp(1) and sample sizen = 5. Explain your results.Problem 4. Consider the z-test (slides 35–37):(a) (4 points) Build the distribution of p-values when H0 is true. Please consider differentdistributions.(b) (8 points) Build the distribution of p-values when H0 is false. Please consider differentdistributions. Try to decrease the sample size, while holding the mean thesame. Try to increase the mean while holding the sample size the same. Explainyour results.(c) (4 points) Build the distribution of p-values when xi ～ Cauchy and sample sizen = 1000. Explain your results.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