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MAST20005/MAST90058: Assignment 2Due date: 10am, Friday 14 September 2018Instructions: Questions labelled with ‘(R)’ require use of R. Please provide appropriate Rcommands and their output, along with su cient explanation and interpretation of the outputto demonstrate your understanding. Such R output should be presented in an integratedform. together with your explanations; do not attach them as separate sheets. Allother questions should be completed without reference to any R commands or output, except forlooking up quantiles of distributions where necessary. Make sure you give enough explanationso your tutor can follow your reasoning if you happen to make a mistake. Please also try tobe as succinct as possible. Each assignment will include marks for good presentation and forattempting all problems.Problems:1. Consider question 2(b) from Assignment 1. Calculate a 95% con dence interval for .2. The blood alcohol content (BAC) of a person will rise after drinking alcoholic drinks suchas beer or wine. Each person’s BAC responds di erently based on many physiologicalfactors. In Australia, a person must have a BAC lower than 0.05 in order to legally drive.(a) You wish to do a study of the impact of drinking on whether people can legallydrive. You wish to estimate the proportion of people who can legally drive half anhour after drinking four standard drinks of beer. To have 95% probability of gettingsuch an estimate to within 0.1 of the true proportion, how many people would youneed to enrol in your study?(b) A new drug has been developed that rapidly digests alcohol and thus reduces people’sBAC. You wish to conduct a trial of this drug to assess its claimed e ect. You willrepeat the same test as above (four standard drinks, measure BAC after half anhour) for n people who take the drug and another n who will not take the drug.You will then compare the proportion of people who can legally drive in each groupby calculating a 95% con dence interval for the di erence in proportions. What ndo you need in order to be able to con dently detect a 0.1 di erence in proportionswith 95% probability (e.g. by the interval being narrow enough to exclude zero)?(c) Your colleague suggests that you should compare the di erence in BAC directlyrather than whether the study subjects can legally drive or not. Suppose thatthe BAC of people under the study conditions who do not take the drug has aN(0:04;0:012) distribution.i. Suppose the drug reduces the mean BAC by and does not change the variance.What value of leads to a 0.1 increase in the proportion of people who canlegally drive?ii. Assuming this is the true value of , what value of n do you need in orderfor a 95% con dence interval to exclude zero? (Assume you know the common= 0:01, but not the population means.)3. (R) Enter the following command in R to access the Animals dataset:> data(Animals, package = &"MASS&")1(Note that this requires the MASS package; if you don’t have it yet, install it rst.) Youwill now have a variable called Animals in your R session which is a data frame. withmeasurements of the average body weight (kg) and average brain weight (g) of variousanimals.(a) We wish to t a simple linear regression model to relate these two measurements,but the raw data are unsuitable for this in their current form. Why?(b) Take the logarithm of all of the measurements and t a simple linear regressionmodel (show an appropriate summary of the model t). Explore the model t viarelevant diagnostic plots. What do you notice?(c) Omit three animals that are clearly di erent from the rest, re t the regression model(again, show an appropriate summary). Show a plot of the data and regression linetogether.(d) Give a 95% con dence interval for the average brain weight of camels that weigh onaverage 500 kg.4. Plants convert CO2 in the atmosphere, along with water and energy from sunlight, into theenergy they need for growth and reproduction. Experiments were performed with normalair atmospheric conditions and those with enriched CO2 concentrations to determine thee ect on plant growth. The plants were given the same amount of water and light fora four week period. The following table summarises the data for the plant growths ingrams.Condition Sample size Mean Standard deviationNormal air 12 4.16 0.914Enriched air 8 5.11 2.592Based on these data, determine whether CO2 enriched atmosphere increases plant growth.5. (R) Let p1 be the proportion of babies with low birth weight (below 2.5 kg) in Africa andp2 be the proportion in the Americas. Respective random samples from each continent,of size n1 = 900 and n2 = 700, gave y1 = 140 and y2 = 80 babies with a low birthweight. Is there evidence that the rates di er between the two continents? Set this up asa hypothesis test.(a) State appropriate null and alternate hypotheses.(b) Carry out a test that has signi cance level = 0:05. What is your conclusion?(c) What would be your decision if = 0:01?(d) Give a 95% con dence interval for the di erence in rates.6. (R) Consider a geometric random variable X with pmfPr(X = xjp) = p(1 p)x; x = 0;1;2;:::A single observation of such a variable is used to test H0 : p = 0:3 against H1 : p = 0:1.The null hypothesis is rejected if the observed value is greater than or equal to 4.(a) What is the probability of committing a Type I error?(b) What is the probability of committing a Type II error?(c) Draw a power curve for this test for all possible alternative values of p (not just 0.1).(d) Find a test of these hypotheses that has an approximate signi cance level of 0.05.What is the actual signi cance level of your test?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