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AUT University STAT500: myexam53
Name:
Student ID:
Note on online assessment conduct
You will have received advice on appropriate and inappropriate conduct for online time-restricted
assessments. But to reiterate:
acceptable Using the R help system for hints
acceptable Referring to lab and lecture notes
acceptable Referring to online education resources
unacceptable Emailing classmates asking for help during the assessment time period
Instructions: (Read all of these instructions carefully).
• Attempt ALL questions.
• This is an open-book assessment.
• You will be required to use R and are permitted (furthermore encouraged!) to use the R
help system.
• Copy this file into Word. The easiest way to do this is to open the document from inside
Word: File > Open, then select the pdf file. Alternatively, open this file in Adobe Acrobat
Pro, 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).
• Remember to keep referring back to the pdf file in case you accidentally delete text or
alter 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-paste
commands and output from an R session).
• Any question involving regression will score 0 marks unless a scattergraph is produced.
stat500: myexam53 3
1. 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 some
patients:
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 this
context
(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 find
2. The probability of a student passing statistics is known to be 0.53; and the probability of a
student passing chemistry is known to be 0.51. If the probability of passing both is known
to 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 study
skills. Of these 29, only 5 fail both. State a sensible null hypothesis, test it, and
interpret.
3. Random variable X is drawn from a normal distribution with mean 10.47 and standard
deviation 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 fair
coin 84 times. It lands heads 45 times.
Is there evidence to support the person’s claims?
(a) State a sensible null hypothesis
(b) State the precise definition of p-value and explain what “more extreme” means in this
context
(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 answer
with the exact binomial p-value above.