Assignment Specification
Question 1
HINT: We cover this in Lecture 1 (Summary Statistics and Graphs)
Data were collected on the prices of parts at each shelf in auto parts showroom in Melbourne. The prices of parts at each shelf, are given below.
50 60 100 120 300 250 400 320 630 200 120 130
60 30 20 10 100 120 139 140 530 450 400 420
550 230 53 120 140 170 180 170 150 190 130 200
100 120 130 140 430 200 200 300 250 140 140 150
160 140 190 230 240 250 260 270 280 290 300 310
Tasks:
a. Construct a frequency distribution using 10 classes, stating the Frequency, Relative Frequency, Cumulative Relative Frequency and Class Midpoint
b. 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
HINT: We cover this in Lecture 2 (Measures of Variability and Association)
You are the manager of a baggage's showroom in the Airport. You are wondering if there is a relation between the number of flights at the airport each day, and the number of baggage's sold. That is, do you sell more baggage's when there are a lot flights, and less when the airport is quiet? If there is a relationship, you might want to keep more baggage's in stock when airport is busy over the upcoming holiday. With the help of the old airport flights schedule, you have compiled the following list covering 7 weeks:
Number of flights at the airport Number of baggage's sold
30 30
20 35
25 33
27 35
32 43
33 40
34 37
Tasks:
a. Is above a population or a sample? Explain the difference.
b. Calculate the standard deviation of the number of flights at the airport. Show your workings. (Hint
- remember to use the correct formula based upon your answer in (a).)
c. Calculate the Inter Quartile Range (IQR) of the number of baggage's sold. When is the IQR more useful than the standard deviation? (Give an example based upon number of number of baggage's sold.)
d. Calculate the correlation coefficient. Using the problem, we started with, interpret the correlation coefficient. (Hint - you are the showroom manager. What does the correlation coefficient tell you? What would you do based upon this information?)
Question 3
HINT: We cover this in Lecture 3 (Linear Regression)
You are the manager of a baggage's showroom in the Airport. You are wondering if there is a relation between the number of flights at the airport each day, and the number of baggage's sold. That is, do you sell more baggage's when there are a lot flights, and less when the airport is quiet? If there is a relationship, you might want to keep more baggage's in stock when airport is busy over the upcoming holiday. With the help of the old airport flights schedule, you have compiled the following list covering 7 weeks:
Number of flights at the airport Number of baggage's sold
30 30
20 35
25 33
27 35
32 43
33 40
34 37
Tasks:
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 there is a holiday? What happens when 10 extra flights arrived?)
b. Calculate AND interpret the Coefficient of Determination.
Question 4
HINT: We cover this in Lecture 4 (Probability)
You are the leader of a cricket team. Some of your players are recruited in-house (that is, from your club members) and some are from other clubs. 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 club members
|
40
|
100
|
|
External recruitment
|
50
|
20
|
Tasks (show all your workings):
a. What is the probability that a randomly chosen player will be from your club members 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 club members, 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
HINT: We cover this in Lecture 5 (Bayes' Rule)
An electronic company is considering launching one of 3 new products: TV, Radio or LCD screens, for its existing market. Prior market research suggest that this market is made up of 4 consumer segments: segment A, representing 60% of consumers, is primarily interested in the functionality of products; segment B, representing 20% 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 10% of the customers (segment D) are after services conscious.
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 TV is 30%
- The probability that a person from segment B prefers TV is 40%
- The probability that a person from segment C prefers TV is 50%
-The company would like to know the probably that a consumer comes from segment A if it is known that this consumer prefers TV over Radio.
Question 6
HINT: We cover this in Lecture 6
A festival sells 2 million tickets at 2$ each. Let the random variable X denote the amount won for a ticket that is purchased. Shown below is the distribution of x. compute the mean and standard deviation of the amount won per ticket. Interpret the mean value. What is the expected profit from the festival?
Distribution of festival winnings
|
Prize (x)
|
Probability P(x)
|
|
1000$
|
0.00004
|
|
100
|
0.00070
|
|
20
|
0.00530
|
|
10
|
0.00711
|
|
4
|
0.02003
|
|
2
|
0.09180
|
|
1
|
0.12350
|
|
0
|
0.76417
|
Question 7
HINT: We cover this in Lecture 7
The average speed of passenger trains travelling from Kyoto to Tokyo have been found to be normally distributed with a mean of 250 km per hour and a standard deviation of 30 km per hour.
a. What is the probability that a train will average less than 200 km per hour?
b. What is the probability that a train will average more than 300 km per hour?
c. What is the probability that a train will average between 210 and 280 km per hour?
Question 8
Having used people-counting devices at the entry to shopping centre, it is known that the average number of shoppers visiting this centre during any one-hour period is 448 shoppers, with a standard deviation of 21 shoppers. What is the probability that a random sample of 49 different one-hour shopping periods will yield a sample mean between 441 and 446 shoppers?