Question 1                                                                                       4 Marks

Visit the Australian Stock Exchange website, www.asx.com.au and from “Prices and research” drop-down menu, select “Company information”. Type in the ASX code “NAB” (National Australia Bank), and find out details about the company. Also, type in the ASX code “WBC” (Westpac Banking Corporation), and find out the details about that company. Information available in the ASX website will be inadequate for your purpose, you will need to search the internet for more information. Your task will be to get the opening prices of NAB and WBC shares for every quarter from January 2009 to December 2017 (unadjusted prices). If you are retrieving the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2009 to 2017 (Total 36 observations). After you have researched share prices, answer the following questions:

  • List all the quarterly opening price values in two tables, one for NAB and the other for WBC. Then construct a stem-and-leaf display with one stem value in the middle, and NAB leaves on the right side and WBC leaves on the left side. (Must use EXCEL or similar for the plot.)        1 mark
  • Construct a relative frequency histogram for NAB and a frequency polygon for WBC on the same graph with equal class widths, the first class being “$14 to less than $16”. Use two different colours for NAB and WBC. Graph must be done in EXCEL or similar software. 1 mark
  • Draw a bar chart of market capitals (or total assets) in 2017 (in million Australian dollars) of 6 companies listed in ASX that trade in similar products or do similar business as NAB or WBC with at least AUD50 million in market capital. Graphs must be done in EXCEL or with similar software.                                                                                                                                            1 mark
  • If one wishes to invest in NAB or WBC, what is the market recommendation (for example, from Morningstar, Fatprophets, InvestSmart, etc.)? If you cannot find the information, what would be your recommendation based on your research of these two companies (trend, P/E ratio, dividend yield, debt and Beta)?                                                                                                      1 mark

Question 2                                                                                       4 Marks

The table below lists the new motor vehicles sales between January 2016 and December 2016 in 8 Australian states.

The complete data are available on the website http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/9314.0December%202017?OpenDocument.

New motor vehicles sales by State between Jan 2016 and Dec 2017

Month State
NSW VIC QLD SA WA TAS NT ACT
Jan-2016 28392 22426 17193 5208 7861 1298 626 1509
Feb-2016 32633 26782 18711 5988 8725 1319 851 1528
Mar-2016 35963 27716 21470 6087 9054 1515 1023 1550
Apr-2016 29391 23963 17753 5174 7601 1313 969 1563
May-2016 32867 26125 19565 5949 7935 1503 1180 1560
Jun-2016 43449 34262 27270 7613 10749 1853 1240 1542
Jul-2016 30219 25517 18445 5210 8234 1389 831 1524
Aug-2016 31788 27096 18062 5785 8144 1743 881 1519
Sep-2016 34424 28766 19702 6551 8668 2074 880 1531
Oct-2016 31850 27546 16870 5450 7580 1937 713 1552
Nov-2016 32955 28991 18733 6259 7657 1903 808 1570
Dec-2016 33632 27065 19252 6464 8026 1918 734 1573

 

From the information provided in the table above,

  • Calculate the mean and standard deviation for each state. 1 mark
  • Calculate the Minimum, Q1, Median, Q3 and Maximum values for each state. 1 mark
  • Draw a box and whisker plot for the number of new vehicles sales of each state and put them side by side on one graph with the same scale for comparison. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.)                                                                                                               1mark
  • Discuss the number of new vehicles sales of each state, and the trends in new vehicles sales in different Australian states.    1 mark

Question 3                                                                                       4 Marks

The Table below is taken from the Australian Bureau of Statistics (ABS) website. It provides data on Australian households with internet access at home from the Household Use of Information Technology Survey.

 

 

From the information provided in the table above,

  • What is the probability that a randomly selected household lives in Victoria? 1 mark
  • What is the probability that a randomly selected household lives in Tasmania and has an internet access in the year 2010-11? 1 mark
  • Given that a household has an internet access in 2012-13, what is the probability that a randomly selected household lives in New South Wales? 1 mark
  • What is the probability that a randomly selected household has an internet access in 2010-11 or 2012-13?1 mark

Question 4                                                                                                             4 Marks

  • In a study conducted by a bus transportation company, the average time of bus arrival at the central station is normally distributed, with a mean of 73 minutes and a standard deviation of 8 minutes. What value does the upper 5% of the time exceed? 1 mark
  • The Bureau of Meteorology found that the air temperature varies uniformly between 12 degree Celsius and 25 degree Celsius. What is the probability that the air temperature will be less than 21 degree Celsius? 1 mark
  • A marketing company is conducting an experiment in which participants are to taste one of two different brands of coffee. Their task is to correctly identify the brand tasted. A random sample of 200 participants is taken and it is assumed that the participants have no ability to distinguish between the two brands.

(i) What is the probability that the sample percentage of correct identifications is greater than 65?   1 mark

(ii) What is the probability that the sample will have between 50% and 60% of the identifications correct?   1 mark

Question 5                                                                                                             4 Marks

  • A survey conducted by a pharmaceutical company found that the probability of success in the clinical trial is 0.70. Suppose five hundred clinical trials are performed in the study, what is the probability of succeeding in the clinical trial between 280 and 355 times? Use normal approximation of the binomial distribution. 1 mark
  • A travel agency acts as a selling agent for a major airline company. The agency found that 210 out of 500 travellers cancelled their airline bookings after they had selected their flight details. At 0.01 level of significance, is there evidence that the population proportion of travellers who select their flights and cancel their bookings is less than 0.50?…………………………………………………………………………………………… 5 mark
  • An internet service provider wants to estimate the mean amount of time that customers spend browsing web sites on daily basis. Find the 95% confidence interval estimate of the mean given the following random sample (in minutes) of 110, 123, 80, 131, 105, 65, 84, 118, 1.5 mark

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