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# HA1011 Applied Quantitative Methods

## Purpose:

This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:

1. Summarise numerical data and present it both by means of tables and charts
2. Be able to calculate and interpret descriptive summary measures
3. Develop simple regression models and interpret the regression coefficients
4. Understand basic probability concepts
5. Understand when to apply different distributions, their properties and how to calculate associated probabilities

## Assignment Structure should be as the following:

Instructions:

• Your assignment must be submitted in WORD format only!
• When answering questions, wherever required, you should copy/cut and paste the Excel output (e.g., plots, regression output etc) to show your working/output.
• Submit your assignment through Safe-Assign in the course website, under the Assignments and due dates, Assignment Final Submission before the due date.
• You are required to keep an electronic copy of your submitted assignment to re-submit, in case the original submission is failed and/or you are asked to resubmit.

## Attempt all the questions (5×8 = 40 Marks)

Question 1

Financial analysts reviewing travel and entertainment costs might have the business objective of determining whether meal costs at city restaurants differ from meal costs at suburban restaurants. They collect data from a sample of 50 city restaurants and from a sample of 50 suburban restaurants for the cost of one meal (in \$).

City Restaurant Meal Costs:

Suburban Restaurant Meal Costs:

1. Construct a frequency distribution for both type of restaurants using 10 classes, stating the Frequency, Relative Frequency, Cumulative Relative Frequency and Class Midpoint.

(3 marks)

• Using (a), construct a histogram for both types of restaurants.                       (2 marks)
• Based upon the raw data, what is the mean, median and mode for both types of restaurants?

(3 marks)

## Question 2

You are the manager of a supermarket and concerned about a forthcoming reduction in the annual advertising budget proposed by the owner. You manage many products that all require separate marketing strategies, predominantly supported by advertising. To justify your request for a higher advertising budget, you collected data on annual sales and annual advertising expenditure.

1. Is above a population or a sample? Explain the difference.                            (2 marks)
2. Calculate the standard deviation of the annual sales. Show your workings.    (2 marks)
3. Calculate the Inter Quartile Range (IQR) of the annual advertising expenditure. When is the IQR more useful than the standard deviation? (Give an example based upon annual advertising expenditure.)                                                                          (2 marks)
4. Calculate the correlation coefficient. Interpret the correlation coefficient.     (2 marks)

## Question 3

(We are using the same data set we used in Question 2)

You are the manager of a supermarket and concerned about a forthcoming reduction in the annual advertising budget proposed by the owner. You manage many products that all require separate marketing strategies, predominantly supported by advertising. To justify your request for a higher advertising budget, you collected data on annual sales and annual advertising expenditure.

1. Explain how you select dependent variable (Y) and independent variable (X) between annual sales and annual advertising expenditure.                                           (2 marks)
2. Calculate AND interpret the Regression Equation (Interpret slope and intercept). You are welcome to use Excel to check your calculations, but you must first do them by hand. Show your workings.                                                                                   (3 marks)
3. Calculate AND interpret the Coefficient of Determination.                              (3 marks)

## Question 4

You are the manager of the Holmes Hounds Big Bash League cricket team. Some of your players are recruited in-house (that is, from the Holmes students) and some are bribed to come over from other teams. You have 2 coaches. One believes in scientific training in computerised gyms, and the other in “grassroots” training such as practising at the local park with the neighbourhood kids or swimming and surfing at Main Beach for 2 hours in the mornings for fitness. The table below was compiled:

1. What is the probability that a randomly chosen player will be from Holmes OR receiving Grassroots training?                                                                                                (2 marks)
2. What is the probability that a randomly selected player will be External AND be in scientific training?                                                                                                   (2 marks)
3. Given that a player is from Holmes, what is the probability that he is in scientific training?

(2 marks)

• Is training independent from recruitment? Show your calculations and then explain in your own words what it means.                                                                             (2 marks)

## Question 5

You are an investment manager for a hedge fund. There are currently a lot of rumours going around about the “hot” property market on the Gold Coast, and some of your investors want you to set up a fund specialising in Surfers Paradise apartments.

Last Saturday you attended an auction to get “a feel” for the local real estate market. You decide it might be worth further investigating. You ask one of your interns to take a quick sample of 50 properties that have been sold during the last few months. Your previous research indicated an average price of \$0.9 million but the average price of your assistant’s sample was only \$850 000.

However, the standard deviation for her research was the same as yours at \$270 000.