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business statistics

Questions and Answers of Business Statistics

A fuel company wishes to determine the proportion of cars that fill up using 95-octane petrol. This population proportion needs to be estimated to within 5% and with a 99% level of confidence.
Determine the sample size necessary to estimate μ for the following information.(a) σ = 20 and ME = 2.5 at 99% confidence(b) σ = 10.2 and ME= 1.5 at 95%confidence(c) Values range from 60 to 460,
C-type batteries have a nominal diameter of 26.2 mm. Producing batteries with this value will ensure they fit properly into all toys and appliances that require C-type batteries. A tolerance
A study reveals that the average amount withdrawn at automatic teller machines (ATMs) is $160 per withdrawal. This figure was determined using a random sample of 91 withdrawals at ATMs. The sample
For each of the following sample results, construct the requested confidence interval. Assume thatthe data come from normally distributed populations.(a) n = 14, x̅ = 30, s2 = 17.2; 98% confidence
A regional town-planning department wants to determine the proportion of residential houses in its region that have air conditioning. To do so, a random sample of 80 houses across the region is
The critical values for a particular two-tailed hypothesis test are given to be −1.96 and 1.96. Depending on the sample selected, the calculated test statistic can vary. For each of the following
A candidate is considering nominating for an election to become mayor of a country town. Prior to officially nominating, the candidate decides to conduct a survey to assess their chances of being
For each of the hypothesis statements in problem 9.1, is a two-tailed test or one-tailed test needed? If it is a one-tailed test, indicate if it is a left tailed or right-tailed test.Problem 9.1(a)
Use the information about each of the following samples to compute the confidence interval to estimate p.(a) n = 25 and p̂ = 0.24; 98% confidence interval(b) n = 142 and p̂ = 0.61; 92% confidence
For each of the following, state the null and alternative hypotheses.(a) The mean length of a piece of ribbon increased to above 15 cm.(b) The population proportion is the same as the historical
A national survey of a large supermarket chain is undertaken. Data are collected for the price of a particular brand of natural yoghurt. The data are shown below. Assuming the prices of natural
Many fast-food chains offer a lower priced combinationmeal in an effort to attract budget-conscious customers. One chain tested a burger, chips and drink combination for $6.95. The weekly sales
A research company has been asked to determine the proportion of all restaurants in Western Australia that serve alcoholic beverages. The company wants to be 98% confident of its results, but has no
According to Runzheimer International, organisations are investing an average of $1436 each year per mobile device. A researcher randomly selects 28 organisations and calculates the average amount
According to a survey, the average cost of a fast-food meal (cheeseburger, large chips, medium soft drink) in Christchurch is $7.25. Suppose this figure is based on a sample of 27 different
A coin-operated laundromat is for sale. An investor wants to determine the average daily revenue generated by this business. An estimate of the average daily revenue is to be found using a random
The table presents two price index series, one with 2006 = 100 for the period 2006 to 2014 and the other with 2014 = 100 for the period 2014 to 2020. Construct a single series for the period 2006 to
From 2015 to 2020, the average hourly earnings of production workers in a certain factory went from $9.85 to $17.36, and the consumer price index went from 82.4 to 152.4. What was the percentage
The table summarises the unit sales and prices for a food manufacturer from 2017 to 2020. Using 2017 as the base year, construct an unweighted price index, a Laspeyres index and a Paasche index.
Calculate Paasche price indices for 2019 and 2020 using these data and 2010 as the base year. 2019 price ($) 2019 2010 price ($) 2020 2020 price ($) Item quantity 13 quantity 12 27.80 22.50 28.11
Calculate Laspeyres price indices for 2018?20 from these data. Use 2010 as the base year. 2010 price ($) 2019 price ($) 0.68 2010 2018 price ($) 2020 price ($) Item quantity 21 0.67 0.71 0.50 1.23
Using these price data collected from Hobart supermarkets, compute the unweighted aggregate price index numbers for the four types of meat. Let 2010 be the base year for this market basket of goods.
The table gives the price of a basket of groceries in a certain city from 2014 to 2020. Find the simple index numbers for the data.(a) Let 2014 be the base year.(b) Let 2016 be the base year.Year
The table shows quarterly data for motor vehicle taxes collected by the federal government in Australia for the period March 2013 to March 2020. (a) Develop 2-lag and 4-lag models. (b) Determine the
The monthly time-series data for the number of people employed on a full-time basis are shown in the table. Plot these data. Estimate the following forecasting models: linear trend, quadratic trend
Time-series data for the number of owner-managers of unincorporated businesses in Australia (’000s) are shown in the table. Fit an exponential trend model to the data and forecast the number of
Data for the number of internet subscribers (in thousands) in Australia for June 2015 to December 2019 are shown below. Fit a quadratic trend model to the data and predict the number of internet
The values of purchasing power for the minimum wage in 1997 dollars for the years 1980 to 1997 are shown in the table. Use these data and exponential smoothing to develop forecasts for the years 1981
The table shows monthly ABS data for approvals for residential buildings in South Australia for the period January 2017 to June 2020. Estimate the data using a linear trend model. Forecast the number
These data give monthly figures for standard variable interest rates in Australia over a 4-year period. Use the data to develop an autoregressive model with a 6-month lag. Discuss the strength of the
Shown are Statistics New Zealand quarterly data for the total number of people employed in New Zealand for the period March 2016 to December 2019. Calculate seasonal indices for the data.
The table gives ABS data for finance provided for the construction of dwellings in New South Wales for January 2018 to May 2020.(a) Evaluate how well the following trend models fit the data: linear,
The ABS publishes census information on manufacturing. Included in these figures are quarterly production figures for electricity (million kilowatt hours) for five years. Use the data in the
The following table shows exports of machinery and transport equipment (in millions of dollars) from September of year 1 to April of year 4. Use these data to develop autoregressive models for a
The ABS publishes a series on Australia?s international merchandise imports and exports. The table displays a portion of the data for imports of chemicals and related products from January of year 1
These are retail turnover data for supermarkets and grocery stores in New South Wales for the period August 2018 to June 2020.(a) Use these data to develop forecasts for the above period using a
The table shows quarterly data for household consumption expenditure in Australia for the period from March 2016 to December 2019. Compute the seasonal indices and then use them to deseasonalise the
These are data on two CPI series for food. The first series is for the period 1997 to 2003 with 1990 = 100, and the second is for the period 2003 to 2007 with 2003 = 100. Combine the two into a
The ABS publishes statistics on the exports of various types of agricultural commodities by month. Shown here are the export figures on fresh, chilled and frozen beef and veal (tonnes) for January of
Compute unweighted aggregate price index numbers for each of the given years using 2011 as the base year. 2011 2016 Item 2020 Pork sausage (per kg) Beef roast (per kg) Chicken breast (per kg)
Using these data, compute index numbers for 2017 to 2020 using 2006 as the base year. Year Year Quantity Quantity 2073 2290 2349 2313 2456 2508 2463 2499 2520 2529 2483 2006 2007 2008 2009 2010 2011
The table shows monthly time-series data for short-term visits to the United Kingdom and its territories by Australian residents. (a) Explore trends in these data by using linear and quadratic
Using the data in Combaro.xls on the student website, develop a multiple regression model to predict productivity (Prdtvty) using days absent (DysAbsnt), job satisfaction (JobSat) and unpaid overtime
Jensen, Solberg and Zorn investigated the relationship between insider ownership, debt and dividend policies in companies. One of their findings was that companies with high insider ownership choose
Study the following residual diagnostic graph. Comment on any possible violations of regression assumptions. Normal plot of residuals 25 20 15 10 0어 -5 -10 -15 -20 -2 -1 Normal score Residual
Nowadays, there are a wide range of digital cameras available with many different features and price tags. The following table lists the prices and effective megapixels of some of these cameras.
Use Excel or a calculator to complete parts (a) to (f) for the following data. (a) Determine the equation of the least squares regression line to predict y using x. (b) Obtain the predicted values
An investor wants to know whether the distribution of weekly rental values in a certain location is normal. The results of her test are as shown. Discuss the test used, the hypotheses, the results
An accounting firm studied the time its accountants took to complete each client?s tax return and related this to the amount of tax paid by the client. The firm wants to know whether a relationship
A computer manufacturer is considering sourcing supplies of an electrical component from one of four different manufacturers. The purchasing manager asks for 95 samples from each of the
The following is a 3 ? 2 contingency table for annual farm profit and the age of the farmer for a randomly selected sample of farmers in Fiji. Use an appropriate test to determine whether annual farm
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

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