Quantitative method

Project description

Quantitative Methods 1

Assignment 3: Inference & Hypothesis Testing

This assignment has three questions, and is due by 5.00pm on Friday May

29. It is to be submitted electronically as a .pdf file using the assignment tool on

the subjects LMS page. Marks depend on your tutor being able to understand

your statements and arguments, so marks may be deducted for poor presentation

or unclear language. Use nothing smaller than 12 point font. If you wish

to write your assignment by hand and scan the file into a .pdf format, you may,

though any illegible content will not be marked. Note that you can only submit

one file, and cannot submit a file larger than around 10 megabytes.

You may work in groups of up to 4 students from the same allocated

tutorial. Groups should nominate one student to submit the assignment for

the whole group, with each students name and student number included in the

document. This assignment has a total of 25 marks available and may contribute

up to 10% of your final mark in this subject.

Question 1: Simulating From The Sampling Distribution

and Interval Estimates (12 Marks)

A disease simulator can be found at the following link:

https://www.learner.org/courses/envsci/interactives/disease/disease.html

The simulator models the spread of a disease across a population over

the course of 100 days. We will be using this application to simulate an

outbreak of Ebola in a high density region. According to research Ebola

has a transmission rate of 15% and is fatal for 60% those infected. Assume

that those infected with the Ebola virus will be contagious for 25 days. Set

these to be the parameter values under the details tab of he application.

Also set the population density to be High.

Run the simulation 30 times and record the proportions of people that die

from each outbreak. (1 Mark).

Compute a histogram of the proportion of deaths that result from each

Ebola outbreak and the four quantities that correspond to the histograms

shape characteristics. If you were able to observe an infinite number of

1

samples (i.e. run the simulation an infinite number of times), what shape

would you expect your histogram of the proportion of deaths to look like?

Why? (4 Marks)

Some news agencies have reported that Ebola kills 90% of those infected.

Evaluate this claim using your data set and confidence intervals. Provide

your reasoning and state your conclusion. 2 Marks)

Now suppose the combination of a new treatment protocol and heightened

vigilance in the population has reduced the transmission rate to only

5%. Using the simulation application and a hypothesis testing framework,

determine whether this reduction in the transmission rate will reduce the

proportion of people dying from Ebola outbreaks. Make sure to outline

all your steps and to provide your reasoning behind each step (5 Marks)

Question 2: Hypothesis Testing (8 Marks)

Joey Walnut is a champion competitive eater known for his unique cupcake

eating technique. Speaking at a press conference in the lead-up to

the coming competitive eating season, Joey claims that his cupcake eating

technique will allow him to consume an average of 50 cupcakes in 5

minutes.

Frame Joeys claim in the language of statistics and specify the way in

which you would go about testing Joeys claim as well as the data you

would require to perform the test. (3 Marks)

Suppose that immediately after Joeys claim, his manager steps in and

asserts that Joey would be able to consume more than 50 cupcakes in 5

minutes on average. How would this change your test? (2 Marks)

Following Joeys press conference, his arch rival Wakeru Sobayashi decides

to hold a press conference of his own in which he claims to have developed

his own cupcake eating technique that will beat Joeys average by 3 cupcakes.

Frame Sobayashis claim in the language of statistics and specify

the way in which you would go about testing Sobayashis claim as well as

the data you would require to perform the test. (3 Marks)

2

Question 3: Bias and Consistency (5 Marks)

You are a junior analyst at a wealth management fund responsible for

evaluating the riskiness of various stocks and portfolios. One day, your

boss sends you a data set of weekly returns on number of different stocks

and asks you to compute a measure of variability for each stock using the

formula

? =

1

n

Xn

i=1

(xi ? x)

2

Where a stock return would be given by xi

What would be the consequence of this approach? Make sure to provide

your reasoning. (3 Marks)

Suggest an alternative approach that might yield a more desirable result.

Make sure to provide your reasoning. (2 Marks)