Reference no: EM133692792

Statistics for Managerial Decisions

Question 1

Visit the Australian Stock Exchange website, www.asx.com.au and from the "Prices and research" drop-down menu, select "Company information". Type in the ASX code "CSR" (CSR Limited), and find out details about the company. Also, type in the ASX code "SFR" (Sandfire Resources NL), and find out the details about that company. Both these companies belong to the material sector. Information available on 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 CSR and SFR shares for every quarter from January 2014 to December 2023 (unadjusted prices). If you are retrieving the monthly prices, read the values at the beginning of every Quarter (January, April, July, October) for every year from 2014 to 2023 (Total 40 observations). After you have researched share prices and the financial sector, answer the following questions:

(a) List all the quarterly opening price values in two tables, one for CSR and the other for SFR. Then construct a stem-and-leaf display with one stem value in the middle, CSR leaves on the right side and SFR leaves on the left side. (Must use EXCEL or similar for the plot.) 1 mark

(b) Construct a relative frequency histogram for CSR and a frequency polygon for SFR on the same graph with equal class widths, the first class being "$2 to less than $3". Use two different colours for CSR and SFR. Graph must be done in EXCEL or similar software. 1 mark

(c) Draw a bar chart of market capitals (or total assets) in 2023 (in million Australian dollars) of 6 companies listed in ASX that trade in similar products or do similar business as CSR or SFR with at least AUD100 million in market capital. Graphing must be done in EXCEL or with similar software.

(d) If one wishes to invest in CSR or SFR, 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)?

Question 2
The table below lists the retail turnover by industry groupbetween January 2023 and December 2023.

Retail turnoverby industry groupbetween Jan 2023 and Dec 2023 (in $ millions)

 

	Turnover
Month	Household goods	Clothing, footwear and personal accessory	Department stores	Other retailing	Cafes, restaurants and takeaway food services
Jan-23	5724.3	2794.1	1687.8	5112.4	5100.2
Feb-23	5160.8	2339.8	1356.7	4728.3	4680.6
Mar-23	5541.5	2722.9	1674.2	5193.6	5343.9
Apr-23	5130.7	2837.2	1820.6	4850.1	5157.9
May-23	5502.7	3005.5	1833.5	5350.0	5325.2
Jun-23	5824.6	2876.4	1777.5	5145.1	5152.1
Jul-23	5432.4	2729.5	1740.5	5165.8	5398.0
Aug-23	5518.6	2732.5	1629.2	5307.7	5494.3
Sep-23	5749.2	2812.7	1782.4	5298.0	5481.3
Oct-23	5969.0	2854.3	1832.3	5471.7	5551.1
Nov-23	6885.5	3455.2	2363.7	6184.4	5463.5
Dec-23	7096.7	4450.6	3189.0	6951.0	5837.4

 

From the information provided in the table above,
(a) Calculate the mean and standard deviation for each industry group.
(b) Calculate the Minimum, Q1, Median, Q3 and Maximum values for each industry group.
(c) Draw a box and whisker plot for the retail turnover of each industry group 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.)
(d) Discuss the retail turnover of each industry group, and the trends.

Question 3
A simple random sample survey of the employees of a large corporation yielded the accompanying table.

 

				Income Level
		Low	Medium		High	Very high	Total
Highest Academic Qualification	Certificate I/II	50	75		30	20	175
	Certificate III/IV	55	105		75	25	260
	Bachelor	40	65		105	35	245
	PhD	20	40		55	45	160
	Total	165	285		265	125	840

 

If a person is chosen randomly in the corporation, then based on the table, answer the following:

(a) What is the probability that the person has bachelor's degree as the highest academic qualification?
(b) What is the probability that the person's income level is Low given that he/she has a PhD degree?
(c) What is the probability that the person has High or Very high-income level?
(d) Is the probability of a person's income independent of his/her highest academic qualification?

Question 4

According to ABS figures, average weekly total earnings of all employees in Australia is $1105 per week. Take this population standard deviation to be $45 per week. If a representative random sample of 70 Australian employees is surveyed, what is the probability the sample average weekly total earnings will be:
(a) less than $1115
(b) more than $1100
(c) between $1110 and $1120
(d) is less than $1098.

Question 5

(a) The Department of Education in Melbourne found that only 50 percent of students attend school in a remote community. If a random sample of 600 children is selected, what is the approximate probability that at least 275 children will attend school? Use normal approximation of the binomial distribution.

(b) A real estate agent randomly selects 100 houses form a population of 1500 houses to appraise the value of houses in that suburb. If the mean appraised value of a house for all houses in this area is $550 000 with a standard deviation of $10 500, what is the probability that the sample average valuation is greater than $560 000?1.

(c) The Melbourne education department surveyed 800 parents to assess those with having financial hardship. It was determined that 18% of the parents suffered some financial hardship of which 10% could not afford the full cost of their child's education. Construct a 99% confidence interval for the proportion of parents who are suffering financial hardship and cannot afford the full cost of their child's education.