Assessment Task â€“ Tutorial Questions Assignment 1

Unit Code: HA1011

Unit Name: Applied Quantitative Methods

Assignment: Tutorial Questions Assessment 1

Due: 11:30pm 15th May 2020

Weighting: 25%

Total Marks: 50 Marks

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

Unit Learning Outcomes Assessed:

1. Understand the pitfalls and benefits of statistics

2. Distinguish between the different survey sampling methods

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

4. Be able to calculate and interpret descriptive summary measures

5. Develop simple regression models and interpret the regression coefficients

6. Understand basic probability concepts

7. Understand when to apply different distributions, their properties and how to calculate associated probabilities

8. Develop confidence interval estimates for the mean and the proportion

9. Perform Hypothesis Tests and interpret the results

Description: Each week students were provided with three tutorial questions of varying degrees of difficulty. These 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 1 to 5 inclusive and submit these answers in a single document.

The questions to be answered are;

Week 1 Question (10 marks)

Based on the following table, calculate the three (3) measures of central locations and briefly discuss what each statistic tells you.

23 30 25 28 36 26 38 45 52 22

33 24 29 41 39 38 48 55 44 19

18 31 34 45 75 61 72 29 27 55

Week 2 Question (10 marks)

Refer to the table below. Consider the relationship between the number of houses sold (Y) and the mortgage rate (X). The values of X and Y for twelve (12) months are shown in the table below.

M-Rates 8 9.5 7.5 11 8.5 10 10.5 7 7.5 11 9 8

Houses sold 188 145 181 137 157 148 140 203 188 144 150 166

Based on that,

a. Calculate the coefficient of correlation between the number of houses sold and the mortgage rate. (6 marks)

b. What does the correlation coefficient tell you about the relationship between the level of house sales and mortgage rates based on the calculation? (4 Marks)

Week 3 Question (10 marks)

In seeking to determine how influential advertising is, the management of a recently established retail chain collected data on sales revenue and advertising expenditure from itsâ€™ stores over the last ten (10) weeks. The table below shows the data collected:

Advertising

Expenditure ($ 000) 3 5 7 6 3.5 4 4.5 7 7.5 8.5

Sales ($ 000) 50 250 700 450 75 150 200 750 800 1,100

a. If they are going to run a linear regression, identify which variable should be the independent variable and which should be the dependent variable in a regression equation. (2 marks)

b. Estimate the slope and intercept coefficients of the linear regression model. (6 marks)

c. If advertising expenditure is equal to $9,000, estimate the total sales income. (2 marks)

Week 4 Question (10 marks)

A retail shop manager analyzed the relationship between sales and the method of payments. Based on his analysis, he has produced the following joint probability table, as shown below:

Size of purchase Method of payment

Cash Credit card Debit Card

Under $20 0.09 0.03 0.04

$20 -$100 0.05 0.21 0.18

Over $100 0.03 0.23 0.14

a. What proportion of purchases were paid by debit card? (2 marks)

b. What proportion of purchases were paid by cash? (2 marks)

c. Determine the proportion of purchases made by credit card or by debit card? (2 marks)

d. Are the events â€œpayment by cashâ€ and â€œpurchase of under $20â€ mutually exclusive?

Explain your answer. (4 marks)

Week 5 Question (10 marks)

a. Given the following probabilities, calculate all the joint probabilities.

P(A) =0.9

P(A) =0.1

P(B/A) =0.4

P (B/ A) =0.7

(4 marks)

b. A coin is flipped three (3) times. Use a probability tree to find the probability of observing: i. No heads

ii. Exactly one head

iii. Exactly two heads iv. At least one tail

(6 marks)

Submission Directions:

The assignment has to be submitted via Blackboard. Each student will be permitted one submission to Blackboard only. Each student needs to ensure that the document submitted is the correct one.

Academic Integrity

Academic honesty is highly valued at Holmes Institute. Students must always submit work that represents their original words or ideas. If any words or ideas used in a class posting or assignment submission do not represent the studentâ€™s original words or ideas, the student must cite all relevant sources and make clear the extent to which such sources were used. Written assignments that include material similar to course reading materials or other sources should include a citation including source, author, and page number.

In addition, written assignments that are similar or identical to those of another student in the class is also a violation of the Holmes Instituteâ€™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 to suspension of enrolment. The penalty would be dependent on the extent of academic misconduct and the studentâ€™s 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, students should refer to their Discussion Board for the unit.

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