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

unacceptable Asking family members or housemates to answer the questions

Instructions: (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 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).

? 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 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.

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