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# HA1011 – Applied Quantitative Methods Group Assignment Attempt all the questions (8x2.5 = 20 Marks) Question 1 of 8 HINT: We cover this in Lecture 1 (Summary Statistics and Graphs) Data were collected...

HA1011 – Applied Quantitative Methods
Group Assignment
Attempt all the questions (8x2.5 = 20 Marks)
Question 1 of 8
HINT: We cover this in Lecture 1 (Summary Statistics and Graphs)
Data were collected on the number of passengers at each train station in Melbourne. The numbers for the weekday peak time, 7am to 9:29am, are given below.
456    1189    410    318    648    399    382    248    379    1240    2268    272
267    1113    733    262    682    906    338    1750    530    1584    7729    323
1311    1632    1606    982    878    169    583    548    429    658    344    2630
538    494    1946    268    435    862    866    579    1359    1022    1618    1021
401    1181    1178    637    2830    1000    2958    962    697    401    1442    1115
a. Construct a frequency distribution using 10 classes, stating the Frequency, Relative Frequency, Cumulative Relative Frequency and Class Midpoint
. Using (a), construct a histogram. (You can draw it neatly by hand or use Excel)
c. Based upon the raw data (NOT the Frequency Distribution), what is the mean, median and mode? (Hint – first sort your data. This is usually much easier using Excel.)
Question 2 of 8
HINT: We cover this in Lecture 2 (Measures of Variability and Association)
You are the manager of the supermarket on the ground floor below Holmes. You are wondering if there is a relation between the number of students attending class at Holmes each day, and the amount of chocolate bars sold. That is, do you sell more chocolate bars when there are a lot of Holmes students around, and less when Holmes is quiet? If there is a relationship, you might want to keep less chocolate bars in stock when Holmes is closed over the upcoming holiday. With the help of the campus manager, you have compiled the following list covering 7 weeks:
Weekly attendance            Number of chocolate bars sold
472                        6 916
413                        5 884
503                        7 223
612                        8 158
399                        6 014
538                        7 209
455                        6 214
a. Is above a population or a sample? Explain the difference.
. Calculate the standard deviation of the weekly attendance. Show your workings. (Hint – remember to use the co
c. Calculate the Inter Quartile Range (IQR) of the chocolate bars sold. When is the IQR more useful than the standard deviation? (Give an example based upon number of chocolate bars sold.)
d. Calculate the co
elation coefficient. Using the problem we started with, interpret the co
elation coefficient. (Hint – you are the supermarket manager. What does the co
elation coefficient tell you? What would you do based upon this information?)
Question 3 of 8
HINT: We cover this in Lecture 3 (Linear Regression)
(We are using the same data set we used in Question 2)
You are the manager of the supermarket on the ground floor below Holmes. You are wondering if there is a relation between the number of students attending class at Holmes each day, and the amount of chocolate bars sold. That is, do you sell more chocolate bars when there are a lot of Holmes students around, and less when Holmes is quiet? If there is a relationship, you might want to keep less chocolate bars in stock when Holmes is closed over the upcoming holiday. With the help of the campus manager, you have compiled the following list covering 7 weeks:
Weekly attendance            Number of chocolate bars sold
472                        6 916
413                        5 884
503                        7 223
612                        8 158
399                        6 014
538                        7 209
455                        6 214
a. Calculate AND interpret the Regression Equation. You are welcome to use Excel to check your calculations, but you must first do them by hand. Show your workings.
(Hint 1 - As manager, which variable do you think is the one that affects the other variable? In other words, which one is independent, and which variable’s value is dependent on the other variable? The independent variable is always x.
Hint 2 – When you interpret the equation, give specific examples. What happens when Holmes are closed? What happens when 10 extra students show up?)
. Calculate AND interpret the Coefficient of Determination.
Question 4 of 8
HINT: We cover this in Lecture 4 (Probability)
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
ibed 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
35
92
External recruitment
54
12
a. What is the probability that a randomly chosen player will be from Holmes OR receiving Grassroots training?
. 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 of 8
HINT: We cover this in Lecture 5 (Bayes’ Rule)
A company is considering launching one of 3 new products: product X, Product Y or Product Z, for its existing market. Prior market research suggest that this market is made up of 4 consumer segments: segment A, representing 55% of consumers, is primarily interested in the functionality of products; segment B, representing 30% of consumers, is extremely price sensitive; and segment C representing 10% of consumers is primarily interested in the appearance and style of products. The final 5% of the customers (segment D) are fashion conscious and only buy products endorsed by cele
ities.
To be more certain about which product to launch and how it will be received by each segment, market research is conducted. It reveals the following new information.
· The probability that a person from segment A prefers Product X is 20%
· The probability that a person from segment B prefers product X is 35%
· The probability that a person from segment C prefers Product X is 60%
· The probability that a person from segment C prefers Product X is 90%
A. The company would like to know the probably that a consumer comes from segment A if it is known that this consumer prefers Product X over Product Y and Product Z.
B. Overall, what is the probability that a random consumer’s first preference is product X?
Question 6 of 8
HINT: We cover this in Lecture 6
You manage a luxury department store in a busy shopping centre. You have extremely high foot traffic (people coming through your doors), but you are wo
ied about the low rate of conversion into sales. That is, most people only seem to look, and few actually buy anything.
You determine that only 1 in 10 customers make a purchase. (Hint: The probability that the customer will buy is 1/10.)
A. During a 1 minute period you counted 8 people entering the store. What is the probability that only 2 or less of those 8 people will buy anything? (Hint: You have to do this by hand, showing your workings. Use the formula on slide 11 of lecture 6. But you can always check your calculations with Excel to make sure they are co
ect.)
B. (Task A is worth the full 2 marks. But you can earn a bonus point for doing Task B.)
On average you have 4 people entering your store every minute during the quiet 10-11am slot. You need at least 6 staff members to help that many customers but usually have 7 staff on roster during that time slot. The 7th staff member rang to let you know he will be 2 minutes late. What is the probability 9 people will enter the store in the next 2 minutes? (Hint 1: It is a Poisson distribution. Hint 2: What is the average number of customers entering every 2 minutes? Remember to show all your workings.)
Question 7 of 8
HINT: We cover this in Lecture 7
You are an investment manager for a hedge fund. There are cu
ently 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 cu
ently sells for \$1.1 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 \$385 000.
There is an apartment up for auction this Saturday, and you decide to attend the auction.
A. Assuming a normal distribution, what is the probability that apartment will sell for over \$2 million?
B. What is the probability that the apartment will sell for over \$1 million but less than \$1.1 million?
Question 8 of 8
HINT: We cover this in Lecture 8
You are an investment manager for a hedge fund. There are cu
ently 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 \$1.1 million but the average price of your assistant’s sample was only \$950 000.
However, the standard deviation for her research was the same as yours at \$385 000.
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?
2
Answered Same Day May 23, 2020 HA1011

## Solution

Pooja answered on May 24 2020
1
data:        a)
456        Class Interval    lower    upper    Fi    R Fi = Fi/N    C. Rfi    Xi (mipdpoint) = (Li+Ui)/2            Row Labels    Count of data:
248        0-349    0    350    10    0.1667    0.1667    175            0-349    10
267        350-699    350    700    20    0.3333    0.5000    525            350-699    20
1750        700-1049    700    1050    10    0.1667    0.6667    875            700-1049    10
1311        1050-1399    1050    1400    8    0.1333    0.8000    1225            1050-1399    8
548        1400-1749    1400    1750    5    0.0833    0.8833    1575            1400-1749    5
538        1750-2099    1750    2100    2    0.0333    0.9167    1925            1750-2099    2
579        2100-2449    2100    2450    1    0.0167    0.9333    2275            2100-2449    1
401        2450-2799    2450    2800    1    0.0167    0.9500    2625            2450-2799    1
962        2800-3149    2800    7700    2    0.0333    0.9833    5250            2800-3149    2
1189        7700-8049    7700    8050    1    0.0167    1.0000    7875            7700-8049    1
379        Grand Total            60    1                    Grand Total    60
1113
530
1632        b)
429        distribution Is POSITIVELY skewed.
494
1359
1181
697
410
1240
733
1584
1606
658
1946
1022
1178
401
318
2268        c)
262        mean    1033.43
7729        median    715
982        mode    401
344
268
1618
637
1442
648
272
682
323
878
2630
435
1021
2830
1115
399
382
906
338
169
583
862
866
1000
2958
Histogram
Fi    0-349    350-699    700-1049    1050-1399    1400-1749    1750-2099    2100-2449    2450-2799    2800-3149    7700-8049    10    20    10    8    5    2    1    1    2    1
2
Weekly attendance     Number of chocolate bars sold
Xi    Yi    (Xi - Xbar)^2    (Yi-Ybar)^2    (Xi-Xbar)*(Yi*Ybar)
472    6916    158.04    12866.04    -1425.96
413    5884    5122.47    843773.47    65743.47
503    7223    339.61    176760.18    7747.90
612    8158    16238.04    1837186.61    172720.33
399    6014    7322.47    621844.90    67479.18
538    7209    2854.61    165184.18    21714.90
455    6214    874.47    346416.33    17404.90
sum    3392    47618    32909.7142857143    4004031.71428571    351384.714285714
a)
Weekly attendance and number of chocolate bars sold is a sample. As there the data is regarding 7 weeks only.
the sample size is 7
b)
mean =      sum(Xi*Fi)/sum(Fi)    484.57
Var =     ...
SOLUTION.PDF