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STAT20029 | Assignment 2 Statistics | Statistics

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Question 1    4 Marks

Visit the Australian Stock Exchange website, 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:

(a)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
(b)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
(c)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
(d)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.

From the information provided in the table above,

(a)Calculate the mean and standard deviation for each state.    1 mark
(b)Calculate the Minimum, Q1, Median, Q3 and Maximum values for each state.    1 mark   
(c)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
(d)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,

(a)What is the probability that a randomly selected household lives in Victoria?    1 mark
(b)What is the probability that a randomly selected household lives in Tasmania and has an internet access in the year 2010-11?    1 mark
(c)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
(d)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

(a)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
(b)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
(c)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)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
(b)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?        1.5 mark
(c)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, 95.     1.5 mark

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