Reference no: EM133522632

Statistics for Managerial Decisions

Question 1 Visit the Australian Stock Exchange website at www2.asx.com.au. 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 2014 to December 2022 (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 2014 to 2022 (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.)

Construct a relative frequency histogram for NAB and a frequency polygon for WBC on the same graph with equal class widths. Use two different colours for NAB and WBC. Graph must be done in EXCEL or similar software.

Draw a bar chart of market capitals (or total assets) in 2022 (in billion Australian dollars) of 6 companies listed in ASX that trade in similar products or do similar business as NAB or WBC with at least AUD 25 billion in market capital. Graphs must be done in EXCEL or with similar software.

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)?

Question 2

The table below lists the retail turnover by industry groups (in $ millions) between January 2022 and June 2023 in Australia.

From the information provided in the table above,

Calculate the mean and standard deviation for each industry group.

Calculate the Minimum, Q1, Median, Q3 and Maximum values for each industry group.

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.)

Discuss the retail turnover of each industry group, and the trends of retail groups in Australia.

Question 3

The Table below is taken from the Australian Bureau of Statistics (ABS) website on the census of population and housing. It provides data on the number of motor vehicles by dwelling structures in the year 2021.

From the information provided in the table above,
What is the probability that a randomly selected flat has two motor vehicles?
What is the probability that a randomly selected separate house has no motor vehicle and three motor vehicles?
What is the probability that a randomly selected caravan has two motor vehicles or four or more motor vehicles?
Given that a dwelling has one motor vehicle, what is the probability that a randomly selected dwelling structure is a cabin?

Question 4
A study of 15 managers at local restaurant suggests that employees who start their work at 9:00am vary their times of arrival uniformly over the range 8:50am to 9:15am. What is the probability that a random accountant arrives between 8:57am and 9:11am?

A local hospital found that the average time for an ambulance service to respond to an incident is normally distributed, with a mean of 17 minutes and a standard deviation of 2 minutes. What value does the upper 5% of the time exceed?

An Internet service provider claims that it can deliver 5,000 hits to a Web site in the next 30 days for only $107.50. If this amount of Web site traffic is experienced, then the time between hits has a mean of 8.64 minutes. Assume that your Web site does get 5,000 hits in the next 30 days and that the time between hits has an exponential distribution. What is the probability that the time between two hits is less than 5 minutes?

Question 5

A local tyre manufacturer performs a durability test on car tyres by driving them over difficult terrain. They found that the probability of success of those car tyres in the durability test is 0.70. Suppose five hundred durability tests are performed in the study, what is the probability of car tyres succeeding in the durability test between 27 and 52 times? Use normal approximation of the binomial distribution.

Wealth Bank wants to estimate the mean amount that bank customers spend on their purchase through the bank mobile apps each week. Find the 95% confidence interval estimate of the mean given the following random sample of $65, $84, $123, $80, $118, $110, $131, $105, $95

A restaurant found that 415 out of 1200 customers cancelled their restaurant reservations after they had reserved their table. At 0.01 level of significance, is there evidence that the population proportion of customers who made their reservations and cancel them is less than 0.30?