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mathematics
business statistics

Questions and Answers of Business Statistics

As part of an infrastructure planning exercise, a city council analyst summarised annual household income and the number of motor vehicles owned for a random sample of households. The results are as
An emergency call service centre keeps records of emergency telephone calls. A study of 150 five-minute time intervals resulted in the following distribution of number of calls. For example, during
The general manager of a cosmetics marketing company believes the annual incomes of its clients are normally distributed. The following data represent the distribution of incomes for a random sample
The human resources (HR) manager of a large IT company has collected data for days of the week on which employees were absent from work. The manager randomly selects 150 of the absences, which are
Four investment companies were asked in a survey to rate the effect on their asset values of a 1 percentage point fall in stockmarket prices. The effect on asset values was rated using a 3-point
A mobile phone store retailer conducts a study to determine whether the number of contracts sold per day by stores is affected by the number of competitors within a 1km radius and the location of the
The table below gives the annual rainfall amounts in millimetres for Melbourne as published by the Australian Bureau of Meteorology (Station No. 086282). Draw a normal probability plot of annual
Suppose an economist is interested in developing a model that predicts total household expenditure as a function of household disposable income. (a) State the independent variable. (b) List at least
According to government figures, the average age of a male federal public servant is 43.6 years and of a male state public servant is 37.3 years. Is there any difference between the variations of
How long do houses for sale remain on the market? One survey reported that, in Sydney, houses for sale are on the market for an average of 112 days. Of course, the length of time varies by the
In a survey of 64 land holdings in the Mossman River catchment, it was found 7.8% of land is used for agricultural production. The corresponding figure for the Daintree River catchment is 6.4% in the
According to the Australian Government, in 2020 there are 485 job service providers listed in Victoria of whom 41 provide job training, and in Queensland there are 382 job service providers of whom
The economic prosperity of a nation is often reflected by the number of people in employment. The Australian Bureau of Statistics (ABS) collects data on the number of people in employment in various
As the prices of heating oil and natural gas increase, consumers become more careful about heating their homes. Researchers want to know how warm home owners keep their houses in July and how the
The Monthly Banking Statistics published by the Australian Prudential Regulation Authority provides selected information on the banking business of individual banks within the domestic market. It
A recent article in the Baycoast City Times states that the days of large backyards have disappeared and that larger properties are in short supply. The journalist writes that the Baycoast region is
A manufacturer of solar power systems is doing some comparative testing of two differently designed 1.9 kWh (10 module) systems. On the basis of a sample of 52 observations, both systems, on average,
A university has collected data to summarise the predominant methods of transportation that students use to travel to the main campus. Students were asked to respond to one category only. In cases
A sales report describes the current price of various digital cameras on the market with 16-megapixel resolution and 10× optical zoom using z-scores. Prices are described as following a normal
A train has been delayed by a fallen tree. The train driver can see the extent of the damage and estimates the probability that the tree will be removed and the train will be able to continue its
A person decides to go to the cinema and has a choice between several movies starting at 3 pm. The person is thinking of seeing one of two action films now showing. What is the probability that they
Determine the mean, variance and standard deviation of the following discrete distribution. Interpretthe mean value.x .............................................. P(x)1
A company that invests heavily in shopping centres conducts a study to determine whether there is a relationship between the type of retailer a customer encounters and whether this occurs on the
Suppose that 20% of all sharemarket investors are retirees. Suppose a random sample of 25 sharemarket investors is taken.(a) What is the probability that exactly 7 are retirees?(b) What is the
Use the Poisson formula to solve the following Poisson distribution problems.(a) If λ = 1.10, what is the probability that x = 3?(b) If λ = 7.57, what is the probability that x ≤ 1?(c) If λ =
Find the following values by using table A.2 in the appendix.(a) P(x = 6|λ = 3.8)(b) P(x > 7|λ = 2.9)(c) P(3 ≤ x ≤ 9|λ = 4.2)(d) P(x = 0|λ = 1.9)(e) P(x ≤ 6|λ
An importer of shirts made in China buys the shirts in lots of 100 from a supplier who guarantees that no more than 2% of the shirts are faulty. On a given day, 15 lots are delivered to the
One of the most useful applications of the Poisson distribution is in analysing visitor numbers on websites. Analysts generally believe visitor numbers (‘hits’) are Poisson distributed. Suppose a
The two most popular majors in a business degree are marketing and international business, with 30% of students enrolled in marketing and 18% enrolled in international business. Suppose 20 students
According to ABS data, 40% of Australians above the age of 65 have chronic heart disease. Suppose you live in a state where the environment is conducive to good health and low stress, and you believe
Find the following values by using the Poisson formula.(a) P(x = 4|???? = 3.2)(b) P(x = 3|???? = 2.3)(c) P(x ≤ 4|???? = 5.1)(d) P(x = 0|???? = 3.5)(e) P(x = 2|???? = 3.7)(f) P(2 < x < 5|????
Solve the following binomial distribution problems by using the binomial formula.(a) If n = 12 and p = 0.33, what is the probability that x = 5?(b) If n = 7 and p = 0.60, what is the probability that
A university conducted a study into students’ perceived usability of a proposed upgrade to the existing learning management system (LMS). Students were asked to visit a test site and evaluate the
A data-management company records a large amount of data. Historically, 0.8% of the pages of data recorded by the company contain errors. If 150 pages of data are randomly selected, what is the
The ABS energy survey reports that 45% of all Australian households have an air conditioner and that 30% of all Australian households have a dishwasher. An Australian household is randomly
Consider the following results of a survey asking, ?Have you visited a museum in the past 12 months?? and ?Do you have a child less than 10 years of age?? Is the variable ?museum visitor?
A company has recently undertaken a program to replace the desktop computers of its staff. The new computers have a different operating system and newer software. Initially, employees appeared
Many organisations, including the Cancer Society of New Zealand, endorse the recommendation that people consume three servings of vegetables and two servings of fruit per day as this provides some
Tropical cyclones are quite common in northern Australia during the summer months. Suppose the number of cyclones is Poisson distributed with a mean of 4.5 cyclones per season.(a) What is the
In any given month, a busy port can have many cargo ships arriving. The following table displays the data collected over a month of ship arrivals at a particular port, with a total of 76. This data
If X is the set of events that lists the seven days of a week, what is the probability that any single day chosen from X will be:(a) A Monday(b) Not a Monday(c) A weekday(d) A weekend day?
Use the values in the contingency table to solve the equations given. (a) P(A ? G) = ___________(b) P(A | G) = ___________(c) P(A) = ___________(d) P(A ? G) = ___________(e) P(F | B) =
A company advertising used cars for sale classifies vehicles, based on their body type, into one of eight mutually exclusive categories. The following table summarises the company’s current range
The following probability matrix contains a breakdown of the age and gender of general practitioners working in Australia. What is the probability that one randomly selected general
A superannuation company offers seven different types of funds that members can choose to invest in. Two of these funds involve a portfolio that exposes investors to a high level of risk. Using only
A survey company asked purchasing managers what traits in a sales representative impressed them most. Seventy-eight per cent selected ‘thoroughness’. Forty per cent responded ‘knowledge of your
A poll is conducted by a television network to evaluate public opinion on the state of the economy in New Zealand using a countrywide representative sample. It is found that 35% of respondents
A white goods manufacturer is sourcing parts for its air-conditioning units. Management is currently putting together a timeline for the next stages of manufacturing. To do so, management considers
Octopus Travel studied the types of work-related activity that Australians do while on holiday. Among other things, 20% take their work with them on holiday. Fifteen per cent negotiate new deals or
An external agency measures the number of listeners of radio stations in a number of different regions. For one particular region in which there are 20 radio stations, it claims that listeners are
A study of tweeting behaviour revealed that, among 36- to 45-year-olds, the number one tweeted topic relates to family, with 28% making some reference to it among those tweets that could be
A government department investigating the issues of tax avoidance and evasion determines that the following outcomes have occurred in a random sample of 400 cases. (a) What is the probability that
Use the values in the following contingency table to solve the equations given. (a) P(A) = __________ (b) P(Z) = __________ (c) P(A ? X) = __________ (d) P(B ? Z) = __________ (e) P(A ? C) =
Convert the following contingency table to a probability matrix to solve the equations given. (a) P(A) = __________(b) P(E) = __________(c) P(A ? E) = __________(d) P(A = E) = __________ 16 в 10 2.
A company is wondering whether a consumer?s preferred brand, among its own and competing brands, is related to the age of the consumer. The company conducts a survey of 2000 consumers, asking
According to the ABS, 73% of women aged 25 to 54 participate in the labour force. Suppose that 78% of women aged 25 to 54 are married or partnered. Suppose also that 61% of all women aged 25 to 54
Given P(A) = 0.40, P(B) = 0.25, P(C) = 0.35, P(B | A) = 0.25 and P(A | C) = 0.80, solve the following.(a) P(A ∩ B) = __________(b) P(A ∩ C) = __________(c) If A and B are independent, P(A ∩ B)
A local GP is concerned that the other doctors in the general practice where she works provide a proportionally higher number of short consultations. A random sample of 200 consultations is extracted
The operations manager of a cinema complex is interested in how patrons using the candy bar purchase food and drinks in various combinations. In particular, the manager wants to know the probability
Given P(A) = 0.10, P(B) = 0.12, P(C) = 0.21, P(A ∩ C) = 0.05 and P(B ∩ C) = 0.03, solve the following equations.(a) P(A ∪ C) = __________(b) P(B ∪ C) = __________(c) If A and B are mutually
Use the values in the following matrix to solve the equations given. (a) P(A ? D) = ?__________(b) P(E ? B) = ?__________(c) P(D ? E) = ?__________(d) P(C ? F) = ?__________ A 12 10 6 8. 2.
According to a recent survey, 40% of millennials (those born in the 1980s or 1990s) view themselves more as ‘spenders’ than ‘savers’. The survey also reveals that 75% of millennials view
According to a consumer report, approximately 3% of New Zealanders bought a new vehicle in the past 12 months. The report also indicates that 10% commenced a new job in the same period. The report
A hardware store determines that 70% of its customers do not use the self-checkout system to make their purchases. It also determines that 80% of its customers pay by credit card. Among those using
The Australian Census of Population and Housing asks every household to report information on each person living in the house. Suppose that, for a sample of 30 households, the number of persons
Determine the mode, median and mean of the following data. 16 9 20 8 17 10 8 2 16 16 19 19 10 4 18
The Australian Census of Population and Housing asks for each resident?s age. Suppose that a sample of 40 households taken from the census data shows the age of the first person recorded on the
The owner of a new Indian restaurant is wondering how its prices compare with others in the local area. Use the following price information on a sample of 16 rogan josh main dishes to write a short
A fitness consultant working with a leading rugby league team measures the height of a sample of 100 male players. The output is broken down by position in terms of summary measures associated with a
Financial analysts like to use the standard deviation as a measure of risk for a stock. The greater the deviation in a stock price over time, the more risky it is to invest in the stock. However, the
Compute the 20th percentile, the 60th percentile, Q1, Q2 and Q3 for the following data. 280 204 820 445 298 320 918 470 964 849 356 450 146 957 800 786
Compute P35, P65, P90, Q1, Q2 and Q3 for the following data. 18 13 29 41 23 29 27 30 11 42 23
A hairdresser franchisor is concerned about the time taken by staff to complete a standard haircut for male customers at one of its newly opened stores. She decides to visit the store and record the
A dataset contains the following seven values. (a) Calculate the range.(b) Calculate the population variance.(c) Calculate the population standard deviation.(d) Calculate the interquartile
The CEO of Combaro would like to know whether employees are satisfied in their positions. In particular, the CEO would like to know about the central tendency of the data and whether they are skewed
The following scatterplot examines the potential association between years of education and weekly salary. The data was obtained from the Combaro dataset on the student website (Combaro.xls). Write
The size in square metres of properties sold by a major real estate firm in Australia in the last year was analysed using descriptive summary measures. The mean size of a one-bedroom residential
A wine industry association reports in its e-newsletter that a particular fine wine is being marketed by online wine distributors with an average market price of $125 per bottle and standard
A car fleet manager working for a local council is thinking of gradually replacing the current fleet of vehicles used by the council with vehicles that use LPG (gas) rather than petrol. The concern
Use the values in the contingency table to solve the equations given. (a) P(F) = ___________(b) P(B ? F) = ___________(c) P(D ? F) = ___________(d) P(B | F) = ___________(e) P(A ? B) =
Suppose Event A occurs 1050 times, Event B occurs 720 times, Event C occurs 120 times and Event D occurs 1110 times. Calculate the relative frequency of each event and report the probabilities of
An online retailer that sells board games and puzzles has produced summary measures, shown in the right-hand column, describing the cost charged to consumers for shipping. Write a short description
A survey of drivers asked respondents to list the age in years of the vehicle that they usually drive. The following data represent a sample of 18 responses provided. Use these data to construct a
A hire car company is interested in summary statistics that are useful in describing travel times between the CBD and the domestic terminal at Sydney Airport. The company locates a report that
According to the Australian Taxation Office, the average taxable income in an affluent suburb of Sydney is $94720. Suppose the median taxable income in this suburb is $90050 and the mode is $89200.
An NRMA report states that the average age of a car in Australia is 10.5 years. Suppose the distribution of ages of cars on Australian roads is approximately bell-shaped. If the standard deviation is
How useful do you think the ability to zoom in on multiple linked graphics is for data analysis? Is it a powerful tool for exploring data and understanding relationships, or is it overcomplicated?
Do you agree with the quote ‘A picture is worth a thousand words. An interface is worth a thousand pictures.’ Why? Why not?
What distinguishes an interactive visualisation from a static visualisation?
What is rescaling?
How does a scatterplot matrix differ from a basic scatterplot?
What is the advantage of using multiple panels in a visualisation?
What visualisation features can be used to represent:(a) categorical information(b) numerical information(c) temporal information?
What is ‘chart junk’? Why do you think it arises?
Describe the advantages of multidimensional visualisation over univariate visualisation.
The following data are monthly downloads (megabytes) on handheld devices. Construct a stemand- leaf plot of the data using the whole part for the stem and the decimal part for the leaf. What does
A researcher wants to determine if the number of international students studying in New Zealand and the number of visitors from their corresponding countries are related. Data on these variables for
Sometimes when we create a stem-and-leaf plot, we get too many leaves per stem to give a good representation of the data. In such a case, we can further split the data space for each stem equally.
The Bureau of Infrastructure, Transport and Regional Economics publishes transport statistics. The table below shows the number of sectors flown by each domestic airline. Construct a pie chart for
The table below shows Department of Foreign Affairs and Trade data for the value (in A$ million) for the top 10 import sources of goods into Australia. Produce a bar chart for these data. On the

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