# STAT20029 T2 2020 Assignment 2

## Assessment item 2—Assignment 2

### Question 1

• List all the quarterly opening price values in two tables, one for NAB and the other for ANZ. Then construct a stem-and-leaf display with one stem value in the middle, and NAB leaves on the right side and ANZ 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 ANZ on the same graph with equal class widths. Use two different colours for NAB and ANZ. Graph must be done in EXCEL or similar software. 1 mark
• Draw a bar chart of market capitals (or total assets) in 2019 (in million Australian dollars) of 6 companies listed in ASX that trade in similar products or do similar business as NAB or ANZ with at least AUD 500 million in market capital. Graphs must be done in EXCEL or with similar software. 1 mark
• If one wishes to invest in NAB or ANZ, 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

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

New motor vehicles sales by State between Jan 2016 - Dec 2016

 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,

(a) 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

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 South Australia? 1 mark
• What is the probability that a randomly selected household has an internet access in 2012-13 or 2014-15? 1 mark
• Given that a household has an internet access in 2010-11, 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 lives in Victoria and has an internet access in the year 2016-2017? 1 mark

### Question 4

• The local police station found that the speed of vehicles travelling around the suburb in the 60 km/hour zone varies uniformly between 55 km/hour and 62 km/hour. What is the probability that the speed of vehicles will be less than 58 km/hour? 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 150 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 70? 1 mark

(ii) What is the probability that the sample will have between 40% and 50% of the identifications correct? 1 mark

• A survey conducted by Burwood train station found that the average time of train arrival at the station is normally distributed, with a mean of 36 minutes and a standard deviation of 3 minutes. What value does the upper 5% of the time exceed? 1 mark

### Question 5

• A family restaurant wants to estimate the mean amount that customers spend on their dinner between Monday and Find the 95% confidence interval estimate of the mean given the following random sample of \$131, \$118, \$95, \$110, \$105, \$65, \$84, \$123, \$80........................................................................................................... 1.5 mark
• A survey conducted by a pharmaceutical company found that the probability of success in the clinical trial is 0.75. Suppose five hundred clinical trials are performed in the study, what is the probability of succeeding in the clinical trial between 275 and 420 times? Use normal approximation of the binomial distribution............................... 1 mark
• An airline company found that 395 out of 800 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 0.45?........................................................................... 5 mark

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