# STAT20029 Statistics for managerial decisions Assessment and Tutor Proposal

## Statistics for managerial decisions

### Assessment criteria

• This assignment must be typed, word-processed or clearly hand-written (but plots and graphs must be done using EXCEL or equivalent software), and submitted online as a single file through Moodle. Important note: The file size must not be over 100MB.
• Microsoft Excel allows students to cut and paste information easily into Microsoft Word documents. Word also allows the use of Microsoft Equation Editor to produce all necessary formulae (use of these are recommended).
• It is expected that Excel would be used to assist in statistical calculations for questions in this assignment. Where Excel is used, use copy function, “Snipping tool” or similar to cut and paste relevant parts of the spreadsheet to verify that you have done the work. (In that case there is no need to write the equations.)
• For those questions where Excel is not used to do the computations, all formulae and working must be included to obtain full marks.
• Only one file will be accepted in any of the formats mentioned above. No zipped file or any other file extension will be accepted.
• There will be late submission penalty for submissions beyond the deadline unless prior approval is obtained from the Unit Coordinator through the extension system in Moodle. Under no circumstances any submission that is late beyond 14 days from the deadline of Friday of Week 10 will be marked, or get any score other than zero.

Assignment markers will be looking for answers which

• demonstrate the student’s ability to interpret and apply the statistical techniques in the scenarios and
• use statistical techniques as decision making tools in the business environment.

Full marks will not be awarded to answers which simply demonstrate statistical procedures without comment, interpretation or discussion (as directed in the questions).

#### Question 1

• List all the quarterly opening price values in two tables, one for TLS and the other for TPM. Then construct a stem-and-leaf display with one stem value in the middle, and TLS leaves on the right side and TPM leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark
• Construct a relative frequency histogram for TLS and a frequency polygon for TPM on the same graph with equal class widths”. Use two different colours for TLS and TPM. Graph must be done in EXCEL or similar software. 1 mark
• Draw a bar chart of market capitals (or total assets) in 2018 (in million Australian dollars) of 5 companies listed in ASX that trade in similar products or do similar business as TLS or TPM 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 TLS or TPM, 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 retail turnover by industry group between January 2018 and December 2018.

The complete data are available on the website

https://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/8501.0Sep%202019?OpenDocument

Retail turnover by industry group between Jan 2018 and Dec 2018 (in \$ millions)

 Turnover Month Household   goods Clothing, footwear   and personal accessory Department stores Other retailing Cafes, restaurants and   takeaway food services Jan-2018 4516.1 1967.4 1413.1 3587.3 3698.8 Feb-2018 4023.6 1632.2 1099.4 3334.5 3377.8 Mar-2018 4327.6 1884.8 1416.2 3651.9 3749.1 Apr-2018 4131.3 1913.2 1402.7 3402.6 3679.3 May-2018 4370.8 2123.9 1518.0 3629.7 3666.6 Jun-2018 4659.6 2099.3 1587.2 3611.7 3601.3 Jul-2018 4420.4 1918.7 1426.7 3721.4 3844.0 Aug-2018 4434.8 1919.5 1343.6 3882.2 3908.3 Sep-2018 4467.8 1915.4 1398.8 3704.7 3863.4 Oct-2018 4779.9 2082.5 1524.8 3965.3 3929.1 Nov-2018 5100.0 2268.7 1745.1 4346.5 3934.2 Dec-2018 5826.5 3351.8 2813.5 5053.1 4278.9

From the information provided in the table above,

• What is the probability that a randomly selected household lives in Queensland? 1 mark
• What is the probability that a randomly selected household lives in Tasmania and accesses the internet for social networking purpose? 1 mark
• Given that a household lives in Victoria, what is the probability that a randomly selected household accesses the internet for formal educational activities? 1 mark
• What is the probability that a randomly selected household has accesses the internet for banking or entertainment?

#### Question 4

• A study conducted by a public transport association found that the average time of bus arrival at the airport domestic terminal is normally distributed, with a mean of 51 minutes and a standard deviation of 4 minutes. What value does the upper 5% of the time exceed? 1 mark
• The height of year 3 students varies uniformly between 110 centimetres and 135 centimetres. What is the probability that the height of year 3 student will be less than 121 centimetres? 1 mark
• A marketing company is conducting an experiment in which participants are to taste one of two different brands of tea. Their task is to correctly identify the brand tasted. A random sample of 250 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 60% and 70% of the identifications correct? 1 mark
•

#### Question 5

• The Department of Education found that sixty two percent of students attend school in a particular urban school district. If a random sample of 500 children is selected, what is the approximate probability that at least 290 children are actually enrolled in school? Use normal approximation of the binomial distribution. 1 mark
• A major travel agency in Australia found that 185 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
• A fine dining restaurant owner wants to estimate the mean amount that the customers spend on their meals in the restaurant. Find the 95% confidence interval estimate of the mean given the following random sample (in dollars) of 210, 125, 80, 131, 105, 65, 84, 118, 95. 1.5 mark

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