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Business Analytics And Statistics 1st Edition Ken Black, John Asafu Adjaye, Paul Burke, Nelson Perera, Carl Sherwood, Saleh A. Wasimi - Solutions
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 follows. Using the chi-square test, determine whether the number of vehicles owned depends on the
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 18 of the five-minute intervals, no calls were received. Use the chi-square goodness-of-fit test and
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 of the company’s clients. Given a sample mean of $67 000 and a standard deviation of $24 000, use
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 shown in the table below. Use α = 0.05 to determine whether these data indicate that absences on the
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 scale, with 1 for no effect, 2 for a slight effect and 3 for a moderate effect. Actual (observed) counts
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 store. The company researchers selected three types of stores for consideration in the study:
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 rainfall amounts and comment on whether the data can be considered to be normally distributed.Year
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 two levels, or classifications, for the variable in part (a). (c) Give the dependent variable for
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 ages of men in the federal sector and men in the state sector? Suppose a random sample of 15 male
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 market. Suppose random samples of 13 houses in Sydney and 11 houses in Brisbane that are for sale are
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 106 holdings surveyed. Construct a 95% confidence interval for the difference in proportion of 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 62 provide job training. Test at a 1% level of significance whether the difference in proportions of
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 sectors. The table below gives the total number of people employed in June 2015 and June 2019 in
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 results from Wollongong and Newcastle compare. The researchers randomly call 23 Wollongong households
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 contains high-level breakdowns of the domestic assets and liabilities of each bank, as well as more
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 the perfect place for those wishing to find houses on larger lots and for property developers to
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, produce 8.18kWh per day. The company is seeking to further develop the system that appears to
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 where multiple methods were used, students were asked to indicate the method that represented the
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 distribution with an average price of $219 and a standard deviation of $13. The z-score associated with
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 journey within the next hour is 90%. This information is communicated to other rail employees at train
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 see both action films at this time? Explain your answer, noting what concept of probability this is
Determine the mean, variance and standard deviation of the following discrete distribution. Interpretthe mean value.x .............................................. P(x)1 ............................................ 0.2682 ............................................ 0.3143
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 ground floor of a shopping complex. A random sample of 550 outlets is tabulated across a number of
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 probability that 10 or more are retirees?(c) How many retirees would you expect to find in a random sample
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 = 3.6, what is the probability that x > 6?
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 = 2.9)(f) P(5 < x ≤ 8|λ = 5.7)
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 importer.(a) What is the probability that, in a given lot of 100 shirts, more than 5 shirts are faulty?(b)
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 large e-commerce website averages 12600 visits per minute.(a) What is the probability that there
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 are selected at random.(a) What is the probability that:(i) at least half of them are studying a
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 the conditions in your state promote healthy hearts. To investigate this theory, you conduct a
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|???? = 3.6)
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 x ≥ 1?(c) If n = 8 and p = 0.80, what is the probability that x > 9?(d) If n = 12 and p =
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 proposed LMS relative to their perceptions of the existing LMS. To further evaluate the results,
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 probability that:(a) 5 or more pages contain errors(b) more than 15 pages contain errors(c) none of 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 selected.(a) Assume that whether a household has a dishwasher is unrelated to whether the same household has
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? independent of the variable ?child under 10?? Why or why not? Visited museum in last year Child under 10 Yes
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 disgruntled about having to learn how to use the computers. The company offered, at great cost, a series
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 protection from heart disease and cancer. A report states that 49% of New Zealanders regularly eat
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 probability of having no cyclones over a season?(b) What is the probability of having between 3 and 4
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 will allow the manager of the port to formulate staffing plans for crews to load and unload the
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) = ___________(f) P(B | F) = ___________(g) P(A ? B) = ___________(h) P(F) = ___________ Н
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 of advertised vehicles.Body type .............................. Number of vehicles for sale4WD/SUV 8
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 practitioner:(a) is 35?44 years old(b) is both female and 45?54 years old(c) is male or is 35?44 years old(d) is
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 this information, what method of assigning probabilities can be used to determine the probability
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 own product’. The purchasing managers were allowed to list more than one trait. Suppose 27% of
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 believe the economy is in an acceptable position. Of the respondents living in rural areas, 75% do not
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 that one set of parts relating to the motor are coming from Germany and one set of parts relating to
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 contracts on holiday. Respondents were allowed to select more than one activity. Suppose that, of
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 fairly random in choosing which station to listen to. Station ABC and Station XYZ are just two of the
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 categorised in a mutually exclusive manner. Other tweets were categorised as referring to the arts (22%),
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 a tax return will be filed? Show how considering the complement of this event provides at least two
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) = __________ (f) P(A ? B) __________ A 42 48 36 18 54 30 12 39 21
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 participants to indicate which brand they prefer and which age group they belong to. The responses to these
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 are married/partnered and participating in the labour force. What is the probability that a randomly
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) = __________(d) If A and C are independent, P(A ∩ C) = __________
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 from the records and the results are detailed in the following contingency table. Calculate the
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 that a patron will purchase water and popcorn, juice and popcorn, soft drink and popcorn, and
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 exclusive, P(A ∪ B) = __________
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 social networking as important to find out about products and services. A social media expert wants to
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 further reveals that in the past 12 months, 2% bought a new vehicle and commenced a new job. A New
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 self-checkout system, however, only 60% pay by credit card.(a) Use this information to determine
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 living in each is reported as follows. Compute the mean, median, mode, range, lower and upper
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 census form as follows. Compute P10, P80, Q1, Q3, the interquartile range and the range of these data.
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 report to the restaurant owner about the central tendency of the data. Restaurant Spice of India
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 sample of 50 players who predominantly play in the forwards and a sample of 50 players who
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 average prices of some stocks are considerably higher than the average prices of others, allowing
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 time taken for such a category of haircut on 30 random occasions. A benchmark of 20 minutes has been
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 range.(e) Calculate the z-score for each value.(f) Calculate the coefficient of variation. 4 8. LO
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 in some way. For instance, the CEO suspects that there may be many employees who are quite satisfied
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 short descriptions about what you would expect to see in the graph and what you actually see. In
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 apartment sold by this firm was 60 square metres, the median was 55 square metres and the standard
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 deviation of $12, with the distribution of prices being approximately bell-shaped. One boutique wine
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 is not so much the average price of petrol but rather the variability in price that occurs, as this
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) = ___________(f) P(B ? C) = ___________(g) P(F | B) = ___________(h) P(A | B) = ___________(i) P(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 each event.(a) P (A) = __________(b) P (B) = __________(c) P (C) = __________(d) P (D) = __________
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 of the data incorporating a discussion of symmetry and skewness to inform the retail owners whether
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 box-and-whisker plot. List the median, Q1, Q3, the endpoints of the inner fences and the endpoints of
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 indicates that the average total time for travel by car is 14 minutes. The shape of the distribution of
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. Is the distribution in this area skewed? If so, how? Which of these measures of central tendency
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 2.4 years, between what two values would 95% of the car ages fall?
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 this plot tell you about monthly downloads on handheld devices? 138.9 138.5 137.5 139.9 139.9 149.9
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 eight Asian countries are shown in the following table. Construct a scatterplot of the data.
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. Suppose 100 CPA firms are surveyed to determine how many audits they perform over a certain time. In
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 these data and comment on your findings.Airline .............................. Number of sectors
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 basis of the charts for this and the previous problem, comment on Australia’s major business
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