HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 1

Assessment Task – Tutorial Questions Assignment

Unit Code: HA1011

Unit Name: Applied Quantitative Methods

Assignment: Tutorial Questions Assignment (Individual)

Due: Week 13 – Friday 26th February, 2021

Weighting: 50%

Purpose:

This assignment is designed to assess your level of knowledge of the key topics covered in this

unit

Unit Learning Outcomes Assessed:

• Summarise numerical data and present it both by means of tables and charts

• Be able to calculate and interpret descriptive summary measures

• Develop simple regression models and interpret the regression coefficients

• Understand basic probability concepts

• Understand when to apply different distributions, their properties and how to calculate

associated probabilities

• Develop confidence interval estimates for the mean and the proportion

• Perform Hypothesis Tests and interpret the results

Description:

Each week students were provided with three tutorial questions of varying degrees of

difficulty. The tutorial questions are available in the Tutorial Folder, for each week, on

Blackboard. The Interactive Tutorials are designed to assist students with the process, skills

and knowledge to answer the provided tutorial questions. Your task is to answer a selection

of tutorial questions for weeks 2 to 11 inclusive and submit these answers in a single

document.

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 2

The questions to be answered are:

Question 1 – Week 4 Tutorial (7 marks)

Use the following data provided in the table below to calculate the correlation “r” between

the price of a product ($) and the quantity of the product purchased per week.

Price ($) Quantity of the Product Purchased per week

10 20

20 15

30 10

30 11

40 9

80 8

90 6

90 4

120 2

130 1

a) Estimate the slope (b1) and intercept coefficients (b0) and write the equation of the

regression line (5 marks)

Step 1: Calculate b1 (3 marks)

Step 2: Calculate b0 (1 mark)

Step 3: Write the equation of the regression line (1 mark)

b) Calculate the coefficient of determination R2 and interpret (2 marks)

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 3

Question 2 – Week 6 Tutorial (7 marks)

A survey of 800 Sydney residents resulted in the following crosstabulation regarding their

major form of transport to work and whether or not they find public transport convenient.

Public Transport

Convenient

(Y/N)

Ferry Bus Train Total

Yes 70 84 126 280

No 182 208 130 520

Total 252 292 256 800

a) What percentage of the Sydney residents have “Bus” as a major form of transport?

(1 mark)

b) What is the probability of selecting a Sydney resident who does NOT find public

transport convenient? (1 mark)

c) Among the Sydney residents who find public transport convenient, what percentage

of residents indicated “Train”? (1 mark)

d) Assuming that a Sydney resident finds public transport convenient, what is the

probability that the resident’s major form of transport is “Ferry”? (2 marks)

e) A randomly selected Sydney resident turns out to be one whose major form of

transport is the Bus. Compute the probability that the Sydney resident does NOT find

public transport convenient. (2 marks)

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 4

Question 3 – Week 7 Tutorial (7 marks)

In a statistics class, a student tosses a biased coin which produces heads only 40% of the time

six (6) times.

a) What is the probability that we get one head? (2marks)

b) What is the probability that we get at most one head? (3 marks)

c) Find the mean and variance. (2 marks)

Question 4 – Week 8 Tutorial (7 marks)

The unit coordinator wants to establish the number of hours students spend studying course

materials on a weekly basis. The hours are normally distributed with a mean of 19.5 and a

standard deviation of 5.2. A random sample of 36 students is taken.

a) What is the probability that the average hours in the sample will be between 17.5 and

21.7? (3 marks)

b) What is the probability that the hours in the sample will be greater than 21.7 (2 marks)

c) What is the probability that the hours in the sample will be less than 20.6 (2 marks)

Question 5 – Week 10 Tutorial (11 marks)

Suppose we know the standard deviation of a certain population is 8. A sample size of 64 has

a mean of 85.

a) Determine the 95% confidence interval estimate of the population mean. (3 marks)

b) Repeat part (a) with a sample size of 100. (3 marks)

c) Repeat part (a) with a confidence interval of 99%. (3 marks)

d) Describe what happens to the confidence interval estimate when:

– the sample size increases.

– Confidence level increases

(2 marks)

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 5

Question 6 – Week 11 Tutorial (11 marks)

A sample of 25 items produced a mean of 46. Assume that the population standard deviation

is 6. Test to determine if we can infer at α = 0.05 that the population mean is less than 50

using the following steps:

a) State the hypotheses. (1 mark)

b) State the relevant test statistic and the reason for the selection. (1 mark)

c) Level of significance. (1 mark)

d) Apply the Decision rule. (4 marks)

e) Calculate test statistics. (2 marks)

f) Provide a conclusion based on the above steps. (2 marks)

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 6

Submission Directions:

The assignment will be submitted via Blackboard. Each student will be permitted only ONE

submission to Blackboard. You need to ensure that the document submitted is the correct

one.

Academic Integrity

Holmes Institute is committed to ensuring and upholding Academic Integrity, as Academic

Integrity is integral to maintaining academic quality and the reputation of Holmes’ graduates.

Accordingly, all assessment tasks need to comply with academic integrity guidelines. Table 1

identifies the six categories of Academic Integrity breaches. If you have any questions about

Academic Integrity issues related to your assessment tasks, please consult your lecturer or

tutor for relevant referencing guidelines and support resources. Many of these resources can

also be found through the Study Skills link on Blackboard. Academic Integrity breaches are a

serious offence punishable by penalties that may range from deduction of marks, failure of

the assessment task or unit involved, suspension of course enrolment, or cancellation of

course enrolment.

Table 1: Six Categories of Academic Integrity Breaches

Plagiarism Reproducing the work of someone else without attribution.

When a student submits their own work on multiple

occasions this is known as self-plagiarism.

Collusion Working with one or more other individuals to complete an

assignment, in a way that is not authorised.

Copying Reproducing and submitting the work of another student,

with or without their knowledge. If a student fails to take

reasonable precautions to prevent their own original work

from being copied, this may also be considered an offence.

Impersonation Falsely presenting oneself, or engaging someone else to

present as oneself, in an in-person examination.

Contract cheating Contracting a third party to complete an assessment task,

generally in exchange for money or other manner of

payment.

Data fabrication and

falsification

Manipulating or inventing data with the intent of supporting

false conclusions, including manipulating images.

Source: INQAAHE, 2020

HA1011 Applied Quantitative Methods – Tutorial Questions Assignment 7

If any words or ideas used the assignment submission do not represent your original words

or ideas, you must cite all relevant sources and make clear the extent to which such sources

were used.

In addition, written assignments that are similar or identical to those of another student is

also a violation of the Holmes Institute’s Academic Conduct and Integrity policy. The

consequence for a violation of this policy can incur a range of penalties varying from a 50%

penalty through suspension of enrolment. The penalty would be dependent on the extent

of academic misconduct and your history of academic misconduct issues. All assessments

will be automatically submitted to Safe – Assign to assess their originality.

Further Information:

For further information and additional learning resources please refer to your Discussion

Board for the unit.