” STAT500程序 写作、 辅导R程序设计程序Name:Student ID:Note on online assessment conductYou will have received advice on appropriate and inappropriate conduct for online time-restrictedassessments. But to reiterate:acceptable Using the R help system for hintsacceptable Referring to lab and lecture notesacceptable Referring to online education resourcesunacceptable Emailing classmates asking for help during the assessment time periodunacceptable Asking family members or housemates to answer the questionsInstructions: (Read all of these instructions carefully). Attempt ALL questions. This is an open-book assessment. You should submit your answers electronically via Blackboard. You will be required to use R and are permitted (furthermore encouraged!) to use the Rhelp system. Copy this file into Word. The easiest way to do this is to open the document from insideWord: File Open, then select the pdf file. Alternatively, open this file in Adobe AcrobatPro, then select File Save As Other Microsoft Word. Save your file. Use a filename that includes your name and student ID number (example:robin_hankin_12345678.doc). Type your answers in this document. Remember to regularly save your file. Upload your work to Blackboard like any other assignment. Remember to keep referring back to the pdf file in case you accidentally delete text oralter the numbering in your Word file.stat500: myexam53 2 Show detailed working, including appropriate mathematical notation for each question.For most questions this will involve showing your working from R, (e.g. cut-and-pastecommands and output from an R session). Any question involving regression will score 0 marks unless a scattergraph is produced.stat500: myexam53 31. A particular demographic of patients is known to have an average blood pressure (MAP)of 63.4 millimeters of mercury. A medical doctor records the MAP blood pressure of somepatients:c(65, 64.7, 73.1, 88.5, 72.9, 65.3)She is unsure whether these patients have higher or lower MAP scores than the NZ average.(a) State a sensible null hypothesis(b) State the precise definition of p-value and explain what more extreme means in thiscontext(c) Is a one-sided or two-sided test needed? justify(d) Perform a student t-test using R and interpret(e) Perform a Z test and account for any differences you find2. The probability of a student passing statistics is known to be 0.53; and the probability of astudent passing chemistry is known to be 0.51. If the probability of passing both is knownto be 0.39, calculate:(a) the probability of failing chemistry(b) the probability of passing at least one of statistics and chemistry(c) the probability of a student passing chemistry, given that they passed statistics(d) Are passing chemistry and statistics independent? Justify(e) (harder) a group of 29 randomly selected students attend a special seminar on studyskills. Of these 29, only 5 fail both. State a sensible null hypothesis, test it, andinterpret.3. Random variable X is drawn from a normal distribution with mean 10.47 and standarddeviation 2.58.(a) Calculate the probability of X being less than 7.51.(b) What is the probability of X exceeding 9.27?(c) What is the probability of X lying between 10.73 and 11.96?(d) Verify your answers to parts 1 and 2 above using numerical sampling.(e) (Harder) verify your answers to part 3 above using numerical sampling.4. A person claims to be able to make make a fair coin land heads more often than expected,using the power of telekenesis. A skeptical scientist investigates this claim and tosses a faircoin 84 times. It lands heads 45 times.Is there evidence to support the persons claims?(a) State a sensible null hypothesis(b) State the precise definition of p-value and explain what more extreme means in thiscontext(c) Is a one-sided or two-sided test needed? justify(d) Using dbinom(), or otherwise, calculate a p-value and interpret.(e) (harder) Calculate a p-value using the normal approximation and compare your answerwith the exact binomial p-value above.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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