Reference no: EM132353379
Applied Quantitative Methods Assignment -
Purpose - Students are required to show the understanding of the principles and techniques of business research and statistical analysis taught in the course.
Assignment Specifications -
Purpose: This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:
1. Explain how statistical techniques can solve business problems.
2. Identify and evaluate valid statistical techniques in a given scenario to solve business problems.
3. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving.
4. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package.
5. Justify and interpret statistical/analytical scenarios that best fits business solution.
Instructions: 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.
Attempt all the questions -
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:
|
27
|
53
|
53
|
65
|
47
|
46
|
47
|
51
|
81
|
57
|
|
30
|
63
|
68
|
29
|
44
|
48
|
57
|
29
|
34
|
42
|
|
53
|
30
|
64
|
88
|
57
|
82
|
51
|
38
|
41
|
32
|
|
55
|
38
|
54
|
57
|
31
|
62
|
44
|
44
|
43
|
53
|
|
63
|
76
|
69
|
45
|
53
|
42
|
45
|
55
|
92
|
92
|
Suburban Restaurant Meal Costs:
|
35
|
33
|
48
|
52
|
58
|
51
|
48
|
40
|
48
|
36
|
|
43
|
42
|
39
|
49
|
38
|
48
|
48
|
56
|
41
|
41
|
|
47
|
30
|
32
|
54
|
32
|
54
|
44
|
48
|
41
|
33
|
|
57
|
34
|
51
|
57
|
42
|
62
|
44
|
29
|
43
|
50
|
|
63
|
72
|
76
|
45
|
53
|
42
|
45
|
55
|
82
|
91
|
Tasks:
a. Construct a frequency distribution for both type of restaurants using 10 classes, stating the Frequency, Relative Frequency, Cumulative Relative Frequency and Class Midpoint.
b. Using (a), construct a histogram for both types of restaurants.
c. Based upon the raw data, what is the mean, median and mode for both types of restaurants?
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.
|
Product
|
Annual Sales ($1000)
|
Annual Advertising Expenditure ($1000)
|
|
1
|
200
|
80
|
|
2
|
200
|
80
|
|
3
|
240
|
120
|
|
4
|
180
|
50
|
|
5
|
170
|
40
|
|
6
|
160
|
40
|
|
7
|
210
|
50
|
|
8
|
230
|
90
|
|
9
|
230
|
110
|
|
10
|
200
|
60
|
|
11
|
210
|
50
|
|
12
|
190
|
80
|
Tasks:
a. Is above a population or a sample? Explain the difference.
b. Calculate the standard deviation of the annual sales. Show your workings.
c. 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.)
d. Calculate the correlation coefficient. Interpret the correlation coefficient.
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.
|
Product
|
Annual Sales ($1000)
|
Annual Advertising Expenditure ($1000)
|
|
1
|
200
|
80
|
|
2
|
200
|
80
|
|
3
|
240
|
120
|
|
4
|
180
|
50
|
|
5
|
170
|
40
|
|
6
|
160
|
40
|
|
7
|
210
|
50
|
|
8
|
230
|
90
|
|
9
|
230
|
110
|
|
10
|
200
|
60
|
|
11
|
210
|
50
|
|
12
|
190
|
80
|
Tasks:
a. Explain how you select dependent variable (Y) and independent variable (X) between annual sales and annual advertising expenditure.
b. 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.
c. Calculate AND interpret the Coefficient of Determination.
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:
|
|
Scientific training
|
Grassroots training
|
|
Recruited from Holmes students
|
28
|
82
|
|
External recruitment
|
45
|
22
|
Tasks (show all your workings):
a. What is the probability that a randomly chosen player will be from Holmes OR receiving Grassroots training?
b. What is the probability that a randomly selected player will be External AND be in scientific training?
c. Given that a player is from Holmes, what is the probability that he is in scientific training?
d. Is training independent from recruitment? Show your calculations and then explain in your own words what it means.
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.
You do some research and discover that the average Surfers Paradise apartment currently sells for $0.9 million. But there are huge price differences between newer apartments and the older ones left over from the 1980's boom. This means prices can vary a lot from apartment to apartment. Based on sales over the last 12 months, you calculate the standard deviation to be $270 000.
There is an apartment up for auction this Saturday, and you decide to attend the auction.
Tasks (show your workings):
A. Assuming a normal distribution, what is the probability that apartment will sell for over $1.5 million?
B. What is the probability that the apartment will sell for over $0.8 million but less than $0.9 million?
Question 6 - 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.
Tasks (show your workings):
A. Since the apartments on Surfers Paradise are a mix of cheap older and more expensive new apartments, you know the distribution is NOT normal. Can you still use a Z-distribution to test your assistant's research findings against yours? Why, or why not?
B. You have over 2 000 investors in your fund. You and your assistant phone 45 of them to ask if they are willing to invest more than $1 million (each) to the proposed new fund. Only 11 say that they would, but you need at least 30% of your investors to participate to make the fund profitable. Based on your sample of 45 investors, what is the probability that 30% of the investors would be willing to commit $1 million or more to the fund?