Assignment 1 QM161 Trimester 3, 2017

Question 1 (20 Marks)

The following monthly expenditures on dairy products were collected from a sample of families in Guyra.

Use your calculator and show your workings to:

(a)Compute the mean, median and mode. (10 Marks)

(b)Compute the range, variance and standard deviation. (10 Marks)

Question 2 (20 Marks)

The following is a stem-and-leaf display representing the weekly rental cost (in $) during the first quarter of 2017, for a sample of 30 tenants renting one-bedroom units in one of the Melbourne's suburbs.

(a)Present a table with the values summarized in the stem-and-leaf display. (5 Marks)

(b)Within what range would you expect 68% of the rental cost for a one-bedroom apartment unit to lie? Justify your answer. (5 Marks)

(c)Find the Z-score for a rental cost of $365. Comment on the relative position of this rental cost in relation to the sample. (5 Marks)

(d)You met a tenant who paid $450 per week. Using the empirical analysis, would you expect this tenant to be renting a one-bedroom unit similar to those in the sample? (5 Marks)

Question 3 (20 Marks)

Information about total net profits earned by 100 wineries in the Hunter Valley during 2016 (in million dollars), is summarised in the following descriptive statistics:

The Box-and-Whisker Plot

Based on the outputs presented above, write a short report about the total net profits earned by wineries in the Hunter Valley during 2016 (maximum 200 words). (20 Marks)

Question 4 (20 Marks)

Households in a city in New South Wales are classified according to suburb and income level, as described in the table below.

Income

Low Medium High

Lake view $50 9,50 1,300

Town 1,000 1,700 500

Green Forest2,000 1,200 850

You plan to run a study randomly selecting one household from this city.

(a)What is the probability that the household is a medium income household? (4 Marks)

(b)What is the probability that the household lives in the suburb "Green Forest"? (4 Marks)

(c)What is the probability that the household lives in the suburb "Town" and has high income? (4 Marks)

(d)What is the probability that the household has a medium income level or lives in the suburb "Lake View"? (4 Marks)

(e)What is the probability that the household has a high income given they live in the suburb "Lake View"? (4 Marks)

Question 5 (20 Marks)

A Market Research company interviewed 500 consumers about their demographics, intention to buy a new mobile phone and brand preferences. 70% of the respondents planned to buy a new mobile phone, from them 50% purchased an "Amazing" brand one, while a 20% from those that did not planned to buy a new mobile phone purchased an "Amazing" brand phone.

(a)Present the probability tree for this problem and calculate all the joint probabilities. (5 Marks)

(b)What is the probability that a randomly selected respondent has purchased an "Amazing" brand mobile phone? (5 Marks)

(c)How many respondents purchased an "Amazing" brand mobile phone? (5 Marks)

(d)What is the probability that a randomly selected respondent that did not plan to buy a new mobile phone ended up purchasing a new "Amazing" brand phone? (5 Marks)